Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

Which of the following is not correct ?

Options:

$\int\limits^{2a}_{0}f(x)dx=\int\limits^{a}_{0}f(x)dx+\int\limits^{a}_{0}f(a-x)dx$

$\int\limits^{b}_{a}f(x)dx=\int\limits^{b}_{a}f(a+b-x)dx$

$\int\limits^{2a}_{0}f(x)dx=2\int\limits^{a}_{0}f(x)dx$ if $f(2a-x)=f(x)$

$\int\limits^{2a}_{0}f(x)dx=0$ if $f(2a-x)=-f9x)$

Correct Answer:

$\int\limits^{2a}_{0}f(x)dx=\int\limits^{a}_{0}f(x)dx+\int\limits^{a}_{0}f(a-x)dx$

Explanation:

$\int\limits^{2a}_{0}f(x)dx=\int\limits^{a}_{0}f(x)dx+\int\limits^{2a}_{a}f(a+x)dx$

$⇒I$ is not correct