First slide

Evaluation of definite integrals

Question

If $\int_{π / 2}^{x} \sqrt{3 - 2 \sin^{2} z} d z + \int_{0}^{y} \cos t d t = 0$ then $\frac{d y}{d x} at (π / 2, π)$ is

Moderate

A

1
B

2
C

$\sqrt{3}$
D

0

Solution

Differentiating w ·r· t· x, we get
$\sqrt{3 - 2 \sin^{2} x} + \frac{d y}{d x} \cos y = 0$
Putting $x = π / 2$ and $y = π$ we get
${\frac{d y}{d x}]}_{(π / 2, π)} = 1 .$

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