Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Choose the correct answer in Exercises 9 and 10. The value of the integral is

Choose the correct answer in Exercises 9 and 10. 

    Q9.    The value of the integral \int_{\frac{1}{3}}^1\frac{(x-x^3)^\frac{1}{3}}{x^4}dx is

                (A)    6

                (B)    0

                (C)    3

                (D)    4

Answers (1)

best_answer

The value of integral is  (A) = 6

\int_{\frac{1}{3}}^1\frac{(x-x^3)^\frac{1}{3}}{x^4}dx
\int_{\frac{1}{3}}^1\frac{(\frac{1}{x^2}-1)^\frac{1}{3}}{x^3}dx\\
let 
\frac{1}{x^2}-1 = t\Rightarrow \frac{dx}{x^3}=-dt/2
now, when x = 1/3, t = 8 and when x = 1 , t = 0

therefore

\\=-\frac{1}{2}\int_{8}^{0}t^{1/3}dt\\ =-\frac{1}{2}.\frac{3}{4}[t^4/3]^0_8\\ =-\frac{3}{8}[-2^4]\\ =6

Posted by

manish

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Fake notice on CBSE 10th, 12th results 2025 in two-halves viral, board alerts students
anam-khan

CBSE Board Result 2025 LIVE: Class 10th, 12th results soon on cbse.gov.in; marksheets, DigiLocker code
anam-khan

CBSE 10th, 12th Results 2025 Live: When will CBSE declare results? Date, time, latest updates

Latest Question