Question

If \[ \frac{dy}{dx} = (x^3-x) -(1-3x^2)\tan x +(x^3-x)\tan^2x \] and \[ y(1)=0, \] then \[ \frac{64}{\pi}y\!\left(\frac{\pi}{4}\right) = ? \]

• A. \(1\)
• B. \(\pi^2+16\)
• C. \(\pi^2-16\)
• D. \(16\pi^2\)

Hint:

When a derivative contains \(\tan^2x\), rewrite it using \[ \sec^2x=1+\tan^2x \] to identify a product-rule pattern.

Answer 1

The Correct Option is C