0

Guest

Courses New

Calculate the area bounded by f(x) = x 2 – x from x = 0 to 2.

Calculate the area bounded by 
f(x) = x2 – x from x = 0 to 2.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

f(x) = x^2 – x
Area ‘A’
A = |\int_{0}^{1}(x^2-x)dx| + \int_{1}^{2}(x^2-x)dx
A = |(\frac{x^3}{3}-\frac{x^2}{2})_{0}^{1}| + \int_{1}^{2}(x^2-x)dx
A = |(\frac{1}{3}-\frac{1}{2})| + \int_{1}^{2}(x^2-x)dx
A = |-\frac{1}{6}| + \int_{1}^{2}(x^2-x)dx
A = \frac{1}{6} + (\frac{x^3}{3}-\frac{x^2}{2})_{1}^{2}
A = \frac{1}{6} + [(\frac{8}{3}-\frac{2^2}{2})-(\frac{1}{3}-\frac{1}{2})]
A = \frac{1}{6} + [\frac{2}{3}-(-\frac{1}{6})]
A = \frac{1}{6} + [\frac{4}{6}+\frac{1}{6})]
A = \frac{1}{6} + \frac{5}{6}
A = 1

Think You Can Provide A Better Answer ?

Other Related Questions on Integral Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More