9. Use a contour integral to evaluate the trigonometric integral. Jo 3+ 2 costat
3. Evaluate the integral S Tz2+9)(x-2) -7x-12dx.
3. (9 marks) Evaluate the integral / V9 – 22 - dx
Evaluate the Integral Evaluate the integral TT " 9 - sin 10x dx 10
– x2 3. (9 marks) Evaluate the integral - dx use the method X =3 sino
Evaluate the following integral. dx 9 F, X 2 49x - 81
9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below. 9. Evaluate o (x+ 1)2 by extending the integral into the complex plane and using the contour C shown below.
(a) Use Trigonometric Substitution to evaluate the integral 22 9 dr. T (b) Use the method of Integration by Parts to rewrite the following integral. (You do not need to fully evaluate the integral.) | «* sin(x2) dr. (c) Find the form of the partial fraction decomposition of 2.r2 - 3.c + 77 (x - 1)(x² +2) (You do not need to solve for the coefficients.)
9. Evaluate the following integral: f xe* dx
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =