Solveeit Logo
Login

Question

Question: If \(\int_{0}^{y}{\cos t^{2}dt}\) = \(\int_{0}^{x^{2}}\frac{\sin t}{t}\)dt. Then \(\frac{dy}{dx}\) i...

If ∫0ycos⁡t2dt\int_{0}^{y}{\cos t^{2}dt} = ∫0x2sin⁡tt\int_{0}^{x^{2}}\frac{\sin t}{t}dt. Then dydx\frac{dy}{dx} is equal to -

A

2sin⁡xxcos⁡y\frac{2\sin x}{x\cos y}

B

2sin⁡x2xcos⁡y\frac{2\sin x^{2}}{x\cos y}

C

2sin⁡x2xcos⁡y2\frac{2\sin x^{2}}{x\cos y^{2}}

D

2sin⁡x2cos⁡y2\frac{2\sin x^{2}}{\cos y^{2}}

Answer

2sin⁡x2xcos⁡y2\frac{2\sin x^{2}}{x\cos y^{2}}

Explanation

Solution

On differentiating under the integral sign,

we get (cos y2) dydx\frac{dy}{dx} = sin⁡x2x2\frac{\sin x^{2}}{x^{2}}.2x

Ž dydx\frac{dy}{dx} = 2sin⁡x2xcos⁡y2\frac{2\sin x^{2}}{x\cos y^{2}}