Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the area of \newline​​the curved trapezoid bounded by the lines y=3x+6y=3x+6, y=0y=0,\newlinex=−1x=-1, x=2x=2. Use integration

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find indefinite integrals using the substitution and by partsright chevron icon

Full solution

Q. Find the area of \newline​​the curved trapezoid bounded by the lines y=3x+6y=3x+6, y=0y=0,\newlinex=−1x=-1, x=2x=2. Use integration
  1. Set up integral: To find the area, we need to integrate the function y=3x+6y=3x+6 between x=−1x=-1 and x=2x=2.
  2. Calculate antiderivative: Set up the integral: A=∫−12(3x+6) dxA = \int_{-1}^{2} (3x+6) \, dx.
  3. Plug upper limit: Calculate the antiderivative: A=[32x2+6x]A = \left[\frac{3}{2} x^2 + 6x\right] from −1-1 to 22.
  4. Plug lower limit: Plug in the upper limit: A=[32×22+6×2]−[antiderivative at lower limit]A = \left[\frac{3}{2} \times 2^2 + 6\times 2\right] - \left[\text{antiderivative at lower limit}\right].
  5. Simplify expression: Plug in the lower limit: A=[32×22+6×2]−[32×(−1)2+6×(−1)]A = \left[\frac{3}{2} \times 2^2 + 6\times 2\right] - \left[\frac{3}{2} \times (-1)^2 + 6\times (-1)\right].
  6. Perform subtraction: Simplify the expression: A=[32×4+12]−[32×1−6]A = \left[\frac{3}{2} \times 4 + 12\right] - \left[\frac{3}{2} \times 1 - 6\right].
  7. Final calculation: Perform the subtraction: A=[6+12]−[1.5−6]A = [6 + 12] - [1.5 - 6].
  8. Area calculation: Final calculation: A=18−(−4.5)A = 18 - (-4.5).
  9. Area calculation: Final calculation: A=18−(−4.5)A = 18 - (-4.5).The area of the curved trapezoid is A=22.5A = 22.5 square units.

More problems from Find indefinite integrals using the substitution and by parts

Question
Evaluate the integral.\newline∫−x4−3xdx \int-x 4^{-3 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫6x3e−2xdx \int 6 x^{3} e^{-2 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫x53xdx \int x 5^{3 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫−2xe2xdx \int-2 x e^{2 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫−2xcos⁡(−2x)dx \int-2 x \cos (-2 x) d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫−xcos⁡(−3x)dx \int-x \cos (-3 x) d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫6x253xdx \int 6 x^{2} 5^{3 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫−6x4−4xdx \int-6 x 4^{-4 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫6x223xdx \int 6 x^{2} 2^{3 x} d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the integral.\newline∫−3xsin⁡(−2x)dx \int-3 x \sin (-2 x) d x \newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

View all (140)