(a)[2]
For $y = \tan^2 x$, show that $\frac{dy}{dx} = 2 \tan x + 2 \tan^3 x$.
(b)[6]
Find the exact value for $\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \left(\tan x + \tan^2 x + \tan^3 x\right)\, dx$.
Mathematics 9709 · AS & A Level · Integration
Mathematics 9709 · AS & A Level · Integration
For $y = \tan^2 x$, show that $\frac{dy}{dx} = 2 \tan x + 2 \tan^3 x$.
Find the exact value for $\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \left(\tan x + \tan^2 x + \tan^3 x\right)\, dx$.