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Math Problems
Calculus
Evaluate definite integrals using the chain rule
Factor completely:
\newline
16
x
2
(
x
−
10
)
−
9
(
x
−
10
)
16 x^{2}(x-10)-9(x-10)
16
x
2
(
x
−
10
)
−
9
(
x
−
10
)
\newline
Answer:
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Nork/en/geometry/unit/
9
9
9
/lesson/
1
1
1
\newline
Coursework
\newline
Edgext
\newline
Wall
\newline
Menu
\newline
Triangle
\newline
△
O
G
K
\triangle OGK
△
OG
K
is shown where
\newline
O
G
=
22.3
OG=22.3
OG
=
22.3
centimeters (cond
\newline
G
K
=
32.5
cm
GK=32.5\text{cm}
G
K
=
32.5
cm
,
O
K
=
21.9
cm
OK=21.9\text{cm}
O
K
=
21.9
cm
. Height of the triangle is
\newline
15
cm
15\text{cm}
15
cm
.
\newline
What is the area of
\newline
△
O
G
K
\triangle OGK
△
OG
K
?
\newline
(A)
\newline
244.185
cm
2
244.185\text{cm}^2
244.185
cm
2
\newline
(B)
\newline
243.75
cm
2
243.75\text{cm}^2
243.75
cm
2
\newline
(C)
\newline
167.25
cm
2
167.25\text{cm}^2
167.25
cm
2
\newline
(D)
\newline
487.5
cm
2
487.5\text{cm}^2
487.5
cm
2
Get tutor help
∫
−
2
2
1
+
x
2
1
+
2
x
d
x
\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x
∫
−
2
2
1
+
2
x
1
+
x
2
d
x
Get tutor help
lim
x
→
π
4
sin
(
2
x
)
−
1
sin
2
(
2
x
)
−
1
\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin (2 x)-1}{\sin ^{2}(2 x)-1}
lim
x
→
4
π
s
i
n
2
(
2
x
)
−
1
s
i
n
(
2
x
)
−
1
Get tutor help
∫
1
9
−
4
x
2
d
x
\int \frac{1}{\sqrt{9-4 x^{2}}} d x
∫
9
−
4
x
2
1
d
x
Get tutor help
∫
0
π
sin
x
d
x
\int_{0}^{\pi} \sin x d x
∫
0
π
sin
x
d
x
Get tutor help
27
27
27
.
∫
0
4
∣
x
2
−
9
∣
d
x
\int_{0}^{4}\left|x^{2}-9\right| d x
∫
0
4
∣
∣
x
2
−
9
∣
∣
d
x
Get tutor help
15
15
15
.
∫
1
2
(
3
x
2
−
1
)
d
x
\int_{1}^{2}\left(\frac{3}{x^{2}}-1\right) d x
∫
1
2
(
x
2
3
−
1
)
d
x
Get tutor help
∫
−
1
0
(
2
x
−
1
)
d
x
\int_{-1}^{0}(2 x-1) d x
∫
−
1
0
(
2
x
−
1
)
d
x
Get tutor help
Solve the Definite integral
\newline
∫
2
3
[
8
x
3
+
3
x
2
+
6
x
]
\int_{2}^{3}\left[8 x^{3}+3 x^{2}+6 x\right]
∫
2
3
[
8
x
3
+
3
x
2
+
6
x
]
Get tutor help
∫
0
2
π
d
x
e
sin
x
+
1
\int_{0}^{2 \pi} \frac{d x}{e^{\sin x}+1}
∫
0
2
π
e
s
i
n
x
+
1
d
x
Get tutor help
∫
0
π
4
sin
3
(
x
)
⋅
cos
(
x
)
d
x
\int_{0}^{\frac{\pi}{4}} \sin ^{3}(x) \cdot \cos (x) d x
∫
0
4
π
sin
3
(
x
)
⋅
cos
(
x
)
d
x
Get tutor help
∫
0
π
4
sin
3
(
x
)
cos
(
x
)
d
x
\int_{0}^{\frac{\pi}{4}} \sin ^{3}(x) \cos (x) d x
∫
0
4
π
sin
3
(
x
)
cos
(
x
)
d
x
Get tutor help
∫
4
d
x
(
x
2
−
2
x
+
5
)
2
\int \frac{4\,dx}{(x^{2}-2x+5)^{2}}
∫
(
x
2
−
2
x
+
5
)
2
4
d
x
Get tutor help
∫
1
3
(
1
ln
(
x
)
)
/
x
d
x
\int_{1}^{3}\left(1^{\ln(x)}\right)/x\,dx
∫
1
3
(
1
l
n
(
x
)
)
/
x
d
x
Get tutor help
∫
1
3
(
7
ln
(
x
)
x
)
d
x
\int_{1}^{3}\left(\frac{7^{\ln(x)}}{x}\right)dx
∫
1
3
(
x
7
l
n
(
x
)
)
d
x
Get tutor help
∫
(
(
1
−
3
x
)
2
x
d
x
\int(\frac{(1-\sqrt{3x})^{2}}{x} dx
∫
(
x
(
1
−
3
x
)
2
d
x
Get tutor help
Evaluate the integral.
\newline
∫
0
7
π
4
tan
(
x
7
)
d
x
\int_{0}^{\frac{7\pi}{4}} \tan \left( \frac{x}{7} \right) dx
∫
0
4
7
π
tan
(
7
x
)
d
x
Get tutor help
Integrate
∫
1
x
4
x
2
−
4
d
x
\int \frac{1}{x^{4}\sqrt{x^{2}-4}}\,dx
∫
x
4
x
2
−
4
1
d
x
Get tutor help
i)
∫
0
1
x
e
2
x
cos
3
(
x
)
d
x
\int_{0}^{1} x e^{2x} \cos^{3}(x) \, dx
∫
0
1
x
e
2
x
cos
3
(
x
)
d
x
Get tutor help
∫
−
1
1
1
2
−
x
d
x
\int_{-1}^{1}\frac{1}{2-x}dx
∫
−
1
1
2
−
x
1
d
x
Get tutor help
What is the product of
(
1
−
p
)
(1-p)
(
1
−
p
)
and
(
1
2
−
p
)
\left(\frac{1}{2}-p\right)
(
2
1
−
p
)
, all reduced by
P
P
P
?
Get tutor help
∫
6
x
−
11
(
x
−
1
)
2
d
x
\int\frac{6x-11}{(x-1)^{2}}dx
∫
(
x
−
1
)
2
6
x
−
11
d
x
Get tutor help
∫
9
x
+
2
x
2
+
x
−
6
d
x
\int\frac{9x+2}{x^{2}+x-6}\,dx
∫
x
2
+
x
−
6
9
x
+
2
d
x
Get tutor help
Evaluate
∫
x
2
+
2
x
+
3
x
+
1
d
x
\int\frac{x^{2}+2x+3}{x+1}\,dx
∫
x
+
1
x
2
+
2
x
+
3
d
x
Get tutor help
∫
1
e
e
tan
−
1
x
x
d
x
\int_{\frac{1}{e}}^{e} \frac{\tan^{-1}x}{x}dx
∫
e
1
e
x
t
a
n
−
1
x
d
x
Get tutor help
∫
0
π
sin
(
3
x
+
π
2
)
d
x
\int_{0}^{\pi}\sin(3x+\frac{\pi}{2})dx
∫
0
π
sin
(
3
x
+
2
π
)
d
x
Get tutor help
∫
10
x
3
−
5
x
x
4
−
x
2
+
6
d
x
\int\frac{10x^{3}-5x}{\sqrt{x^{4}-x^{2}+6}}\,dx
∫
x
4
−
x
2
+
6
10
x
3
−
5
x
d
x
Get tutor help
∫
e
−
x
+
sin
x
e
−
x
+
cos
x
d
x
\int \frac{e^{-x} + \sin x}{e^{-x} + \cos x} \, dx
∫
e
−
x
+
c
o
s
x
e
−
x
+
s
i
n
x
d
x
Get tutor help
∫
e
−
x
+
sin
x
cos
x
+
e
−
x
d
x
\int\frac{e^{-x}+\sin x}{\cos x+e^{-x}}\,dx
∫
c
o
s
x
+
e
−
x
e
−
x
+
s
i
n
x
d
x
Get tutor help
c)
∫
0
1
x
e
2
x
cos
3
(
x
)
d
x
\int_{0}^{1} x e^{2x} \cos^{3}(x) \, dx
∫
0
1
x
e
2
x
cos
3
(
x
)
d
x
Get tutor help
lim
x
→
0
+
(
e
x
2
−
cosh
(
x
)
(
x
+
x
5
)
α
)
\lim_{x \to 0^{+}}\left(\frac{e^{\frac{x}{2}}-\cosh(\sqrt{x})}{(x+\sqrt[5]{x})^{\alpha}}\right)
x
→
0
+
lim
(
(
x
+
5
x
)
α
e
2
x
−
cosh
(
x
)
)
Get tutor help
∫
x
3
d
x
(
x
2
+
1
)
3
2
\int \frac{x^{3} \, dx}{(x^{2}+1)^{\frac{3}{2}}}
∫
(
x
2
+
1
)
2
3
x
3
d
x
Get tutor help
a)
∫
0
π
2
x
sin
x
d
x
\int_{0}^{\frac{\pi}{2}} x \sin x \, dx
∫
0
2
π
x
sin
x
d
x
Get tutor help
Let
f
f
f
be the function defined by
f
(
x
)
=
2
x
f(x)=2^{x}
f
(
x
)
=
2
x
. If six subintervals of equal length are used, what is the value of the right Riemann sum approximation for
∫
2
3.5
2
x
d
x
\int_{2}^{3.5} 2^{x} d x
∫
2
3.5
2
x
d
x
? Round to the nearest thousandth if necessary.
\newline
Answer:
Get tutor help
Let
f
f
f
be the function defined by
f
(
x
)
=
2
x
f(x)=2^{x}
f
(
x
)
=
2
x
. If three subintervals of equal length are used, what is the value of the right Riemann sum approximation for
∫
1
2.5
2
x
d
x
\int_{1}^{2.5} 2^{x} d x
∫
1
2.5
2
x
d
x
? Round to the nearest thousandth if necessary.
\newline
Answer:
Get tutor help
Evaluate
∫
0
20
(
9
e
0.2
x
+
2
)
d
x
\int_{0}^{20}\left(9 e^{0.2 x}+2\right) d x
∫
0
20
(
9
e
0.2
x
+
2
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
4
(
2
e
−
0.25
x
−
4
x
)
d
x
\int_{0}^{4}\left(2 e^{-0.25 x}-4 x\right) d x
∫
0
4
(
2
e
−
0.25
x
−
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
5
(
7
e
−
0.2
x
−
4
x
)
d
x
\int_{0}^{5}\left(7 e^{-0.2 x}-4 x\right) d x
∫
0
5
(
7
e
−
0.2
x
−
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
5
(
3
e
−
0.2
x
−
2
x
)
d
x
\int_{0}^{5}\left(3 e^{-0.2 x}-2 x\right) d x
∫
0
5
(
3
e
−
0.2
x
−
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
10
(
3
e
0.2
x
+
4
)
d
x
\int_{0}^{10}\left(3 e^{0.2 x}+4\right) d x
∫
0
10
(
3
e
0.2
x
+
4
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
4
(
5
e
−
0.25
x
−
4
x
)
d
x
\int_{0}^{4}\left(5 e^{-0.25 x}-4 x\right) d x
∫
0
4
(
5
e
−
0.25
x
−
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
2
(
2
e
0.5
x
−
2
x
)
d
x
\int_{0}^{2}\left(2 e^{0.5 x}-2 x\right) d x
∫
0
2
(
2
e
0.5
x
−
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
4
(
9
e
0.25
x
+
4
x
)
d
x
\int_{0}^{4}\left(9 e^{0.25 x}+4 x\right) d x
∫
0
4
(
9
e
0.25
x
+
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
6
(
10
e
−
0.5
x
−
2
x
)
d
x
\int_{0}^{6}\left(10 e^{-0.5 x}-2 x\right) d x
∫
0
6
(
10
e
−
0.5
x
−
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
5
(
7
e
0.2
x
+
4
x
)
d
x
\int_{0}^{5}\left(7 e^{0.2 x}+4 x\right) d x
∫
0
5
(
7
e
0.2
x
+
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
30
(
2
e
−
0.2
x
−
1
)
d
x
\int_{0}^{30}\left(2 e^{-0.2 x}-1\right) d x
∫
0
30
(
2
e
−
0.2
x
−
1
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
2
(
10
e
−
0.5
x
+
2
x
)
d
x
\int_{0}^{2}\left(10 e^{-0.5 x}+2 x\right) d x
∫
0
2
(
10
e
−
0.5
x
+
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
5
(
3
e
0.2
x
−
2
x
)
d
x
\int_{0}^{5}\left(3 e^{0.2 x}-2 x\right) d x
∫
0
5
(
3
e
0.2
x
−
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
Evaluate
∫
0
2
(
9
e
−
0.5
x
−
4
x
)
d
x
\int_{0}^{2}\left(9 e^{-0.5 x}-4 x\right) d x
∫
0
2
(
9
e
−
0.5
x
−
4
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
Get tutor help
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