Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Calculus
Find indefinite integrals using the power rule (Level 2)
Fill in the table. Find th rule:
\newline
\newline
X
X
X
(input)
\newline
Y
Y
Y
(output
\newline
\newline
1
1
1
\newline
5
5
5
\newline
\newline
3
3
3
\newline
9
9
9
\newline
\newline
4
4
4
\newline
11
11
11
Get tutor help
Find the area
A
A
A
enclosed by the lemniscate with equation
r
2
=
81
cos
(
2
θ
)
r^{2}=81 \cos (2 \theta)
r
2
=
81
cos
(
2
θ
)
. Choose your limits of integration carefully.
\newline
The lemniscate
\newline
(Give your answer to the nearest whole number.)
Get tutor help
Use a suitable change of variables to determine the indefinite integral. (Use
C
C
C
for the constant of integration.)
\newline
∫
(
sin
2
(
θ
)
−
2
sin
(
θ
)
)
(
sin
3
(
θ
)
−
3
sin
2
(
θ
)
)
3
cos
(
θ
)
d
θ
\int\left(\sin ^{2}(\theta)-2 \sin (\theta)\right)\left(\sin ^{3}(\theta)-3 \sin ^{2}(\theta)\right)^{3} \cos (\theta) d \theta
∫
(
sin
2
(
θ
)
−
2
sin
(
θ
)
)
(
sin
3
(
θ
)
−
3
sin
2
(
θ
)
)
3
cos
(
θ
)
d
θ
Get tutor help
7
7
7
.
[
0
/
2
[0 / 2
[
0/2
Points]
\newline
DETAILS
\newline
PREVIOUS ANSWERS
\newline
SCALCE
\newline
Use implicit differentiation to find
∂
z
∂
x
\frac{\partial z}{\partial x}
∂
x
∂
z
and
∂
z
∂
y
\frac{\partial z}{\partial y}
∂
y
∂
z
.
\newline
y
z
=
8
ln
(
x
+
z
)
∂
z
∂
x
=
□
∂
z
∂
y
=
□
\begin{array}{l} y z=8 \ln (x+z) \\ \frac{\partial z}{\partial x}=\square \\ \frac{\partial z}{\partial y}=\square \end{array}
yz
=
8
ln
(
x
+
z
)
∂
x
∂
z
=
□
∂
y
∂
z
=
□
Get tutor help
Which of the following is equivalent to
log
c
(
6
)
log
(
6
)
\frac{\log_{c}(6)}{\log(6)}
l
o
g
(
6
)
l
o
g
c
(
6
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
c
)
\log(c)
lo
g
(
c
)
\newline
(B)
log
c
(
1
)
\log_{c}(1)
lo
g
c
(
1
)
\newline
(C)
1
log
(
c
)
\frac{1}{\log(c)}
l
o
g
(
c
)
1
\newline
(D)
1
log
(
6
)
\frac{1}{\log(6)}
l
o
g
(
6
)
1
Get tutor help
