(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.)
Please show all steps. Evaluate the integral using a trigonometric substitution. Jo (4 – x2) 312 * - *2)3/2 dx
9. Use a contour integral to evaluate the trigonometric integral. Jo 3+ 2 costat
2. (20 points) Evaluate the following integral using Integration by Parts or Trigonometric Substitution dr Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for r as well as dr and other corresponding parts of your substitution
Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) $$ \int \frac{x^{3}}{\sqrt{x^{2}+25}} d x, \quad x=5 \tan (\theta) $$
3. Use the trigonometric substitution r = a sin(0) to evaluate the following indefinite integral: da
2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric substitution to conclude that Evaluate 1- x2 dx by using the FTC and then verify your answer by interpreting the integral as the area of a familar shape. 2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric...
3) Evaluate the following integrals: 13 dx Jo (x2 +93/2 +9)3/2 dr
Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.)
Evaluate the following integral using trigonometric substitution. dx S 3 2 (1+x²) dx S 11 2 (Type an exact answer.)