Evaluate the following integrals.
Problem 14E Evaluate the following integrals. Answer;Step-1 The given integral is By the substitution method we can evaluate the limit . For our convenience let , us take x = 4 sin(p) (or) x = 4 cos(p) Let , x = 4 sin(p) , that implies = sin(p) = , = cos(p) = , and tan(p) = = …………..(1) Then the integrand becomes = = , since = 4. = = , since (p) += 1 , and = 36. = = , since = Therefore , if x = 4 sin(p) , then = ………….(2) And (x) = 4 cos(p) 1 = 4 cos(p) That is , dx = 4 cos(p) dp…………….(3) From (2) , (3) the above integral becomes ; = 4 cos(p) dp = dp , since = = ()dp , since = sec(p) = ()dp , since . = tan(p) +C , since dx = tan(x) +c. = +c , since from(1), tan(p) = Therefore , = +c.