## ExercisesforSection 4: Integrals of Trigonometric Functions

Calculate the following integrals

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

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

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

Calculate the following definite integrals

 29 $\int_{0}^{\pi} \sin x\ dx$ 30 $\int_{0}^{\pi} \cos x\ dx$ 31 $\int_{0}^{\pi/4} \tan x\ dx$

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Last Updated: September, 1996