Q2- Evaluate the integrals: (a) ſ sinᵒ x.cos x. dx (b) ſ sin 8x. sin 5x.dx
Express the integrand as a sum of partial fractions and evaluate the integrals. x+8 -dx 2x3 - 8x Rewrite the integrand as the sum of partial fractions. x+8 2x - 8x Evaluate the integrals. X+8 -dx = 2x3 - 8x
7. Evaluate the following integrals using integration by parts: a xe-ºrd sin (x)dx
1.) Find the definite integrals a.) sdx b.) S dx x2-4x+9 c.) ſ 4arccos xdx d.) Se-3x sin 5xdx e.) S In(4 + x2)dx f.) s cosst dt sin t g.) St tan 5 2xsec 4 2xdx h.) ſ sin(-4x)cos3xdx
Express the integrand as a sum of partial fractions and evaluate the integrals. X + 9 Sauna dx 2x3 - 8x Rewrite the integrand as the sum of partial fractions. X + 9 2x3 - 8x Evaluate the integrals. X + 9 dx = - 8x 273
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
Evaluate the following integrals. (a) / In(3x) dx for x > 0 (e) / ( +er) dx (n lete* dx (e) sin(5x +1) dx
step by step please freda ſ sin sin(x) dx. 3.r? – 112 + 10 dr. 6.2? + 10.2 < V3 - 2.0 - x? dr. In(a) dr if it exists. .c?
4. Given the integrals, [° 8(x) dx =-7, 5*8(x)dx = 6 and 5*g(x) dx = 10, use the properties of integrals to determine the value of the integrals below. a) [°(f(x)+g(x)\dx b) ſ 8(x)dx (4 pts cach) c) $39(x)dx a [ f(x)dx
1. Evaluate the following integrals: 8. x(2x + 3)dx b.