Question

Assertion :The value ${\int }_{-4}^{-5}\sin (x^2-3)dx+{\int }_{-2}^{-1}\sin (x^2+12x+33)$ is zero. Reason: ${\int }_{-a}^{a}f\left(x\right)dx=0$ if f(x) is an odd function.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$I={\int }_{-4}^{-5}\sin (x^2-3)dx+{\int }_{-2}^{-1}\sin (x^2+12x+33)dx=I_1+I_2$
$I_2={\int }_{-2}^{-1}\sin (x^2+12x+33)dx={\int }_{-2}^{-1}\sin \left(\right(x+6{)}^2-3)dx,$
But $x+6=-y$
$\therefore I_2=-{\int }_{-4}^{-5}\sin (y^2-3)dy=-I_1$
or $I_1+I_2=0$ or $I=0$
The reason is true but it does not explain the assertion.
Hence, B is correct