Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

The value of $\int\limits^{1}_{-1}x^2[x]dx$ is :

Options:

$\frac{1}{3}$

$\frac{2}{3}$

1

$-\frac{1}{3}$

Correct Answer:

$-\frac{1}{3}$

Explanation:

The correct answer is Option (4) → $-\frac{1}{3}$

$\int\limits^{1}_{-1}x^2[x]dx$

$=+\int\limits^{0}_{-1}x^2[x]dx+\int\limits^{1}_{0}x^2[x]dx$

$=-\int\limits^{0}_{-1}x^2dx+0$

$=\left[-\frac{x^3}{3}\right]^{0}_{-1}=-\frac{1}{3}$