## ExercisesforSection 4: Integrals of Trigonometric Functions

Calculate the following integrals

 1 ∫ $(\sin x - \cos x) dx$ 2 ∫ $(\tan x + \cos x) dx$ 3 ∫ $cosec(2x - 3) dx$ 4 ∫ $\tan(7x + 2) dx$ 5 ∫ $x cotan(x^2 - 1) dx$ 6 ∫ $(x+1)\cos(x^2 + 2x) dx$ 7 ∫ $\cos x \sin^3x dx$ 8 ∫ $\sin x \cos^4x dx$ 9 ∫ $cosec^2(2x - 3) dx$ 10 ∫ $\sec(2x - 3)\tan(2x - 3) dx$ 11 ∫ $x^{-2} \sin(1/x) dx$ 12 ∫ $\frac{\sin x}{1 + \cos x} dx$ 13 ∫ $\cos x(1 - \sin x) dx$ 14 ∫ $e^x + \sec^2 \frac{x}{e^x + \tan x} dx$ 15 ∫ $e^x \tan(e^x) dx$ 16 ∫ $(x \cos x) dx$ 17 ∫ $(2x - 1)\sin x dx$ 18 ∫ $(x^2- x + 4)\sin(2x) dx$ 19 ∫ $(x^3\cos(x/2)) dx$ 20 ∫ $(e^{2x}\sin x) dx$ 21 ∫ $(e^{-x}\cos x) dx$ 22 ∫ $(\sin x)(\ln \|\cos x\|) dx$ 23 ∫ $(\cos x)(\ln \|\sin x\|) dx$ 24 ∫ $\tan^2x dx$

Verify the following integrals either by computing the integral directly, or by differentiating the answer.

 25 ∫ $cotan x dx = \ln \|\sin x\| + C$ 26 ∫ $\sec x dx = \ln \|\sec x + \tan x\| + C$ 27 ∫ $cosec x dx = -\ln \|cosec x + cotan x\| + C$ 28 ∫ $\sin^2x = 0.5(x - 0.5\sin(2x)) dx$

Calculate the following definite integrals

 29 ∫ $π$$0 \sin x dx 30 ∫ π$$0$ $\cos x dx$ 31 ∫ $π/4$$0$ $\tan x dx$

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Last Updated: September, 1996