LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
15 views
in Calculus by (54.3k points)
closed by
Find the value of \(\rm \int_0^1 x^2(1+x^3)dx\)
1. \(\frac 1 4\)
2. \(\frac 32\)
3. \(\frac 12\)
4. \(\frac 34\)
5. None of these

1 Answer

0 votes
by (30.0k points)
selected by
 
Best answer
Correct Answer - Option 3 : \(\frac 12\)

Concept:

\(\rm \int x^n dx = \frac{x^{n+1}}{n+1}+c\)

Calculation: 

I = \(\rm \int_0^1 x^2(1+x^3)dx\)

Let 1 + x3 = t

Differentiating with respect to x, we get

⇒ (0 + 3x2)dx = dt

⇒ x2 dx = \(\rm \frac {dt}{3}\)

x 0 1
t 1 2


Now,

I = \(\rm \frac{1}{3}\int_1^2 tdt\)

\(\rm \frac{1}{3} \left[\frac{t^2}{2} \right ]_1^2\)

\(\rm \frac{1}{6} [4-1] = \frac{3}{6} = \frac{1}{2}\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...