How do you evaluate the definite integral #int sin^(5)x * cos^(20)x dx# from [0,pi/2]? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Cesareo R. Sep 8, 2016 #1/21-2/23+1/25# Explanation: #int_0^(pi/2) sin^(5)x * cos^(20)x dx =int_0^(pi/2) (1-cos^2x)^2cos^20 x sin x dx# #=int_0^(pi/2) (1-2cos^2x+cos^4x)cos^20 x sin xdx =# #=int_0^(pi/2)(cos^20x-2cos^22 x+cos^24x)sinx dx =# #=-1/21(0-1)+2/23(0-1)-1/25(0-1)=# #=1/21-2/23+1/25# Answer link Related questions What is the Formal Definition of the Definite Integral of the function #y=f(x)# over the... How do you use the definition of the definite integral? What is the integral of dy/dx? What is an improper integral? How do you calculate the double integral of #(xcos(x+y))dr# where r is the region: 0 less than... How do you apply the evaluation theorem to evaluate the integral #3t dt# over the interval [0,3]? What is the difference between an antiderivative and an integral? How do you integrate #3x^2-5x+9# from 0 to 7? Question #f27d5 How do you evaluate the definite integral #int sqrtt ln(t)dt# from 2 to 1? See all questions in Formal Definition of the Definite Integral Impact of this question 5415 views around the world You can reuse this answer Creative Commons License