Question #e63af Calculus Using Integrals to Find Areas and Volumes Definite Integrals with Substitution 1 Answer Narad T. Jan 4, 2017 The answer #==-73/504=-0.14484# Explanation: We need #intx^ndx=x^(n+1)/(n+1)+C(x!=-1)# Therefore, #int_0^1x^6(4x^2+x-5)dx# #=int_0^1(4x^8+x^7-5x^6)dx# #=[4x^9/9+x^8/8-5x^7/7] _0^1# #=(4/9+1/8-5/7)-(0)# #=(224+63-360)/504# #=-73/504=-0.14484# Answer link Related questions How do you do definite integrals with substitution? How do you find the integral #int_1^2e^(1/x)/x^2dx# ? How do you find the integral #int_0^1x*e^(-x^2)dx# ? How do you find the integral #int_0^13dx/(root3((1+2x)^2)# ? How do you find the integral #int_0^1x*sqrt(1-x^2)dx# ? How do you find the integral #int_e^(e^4)dx/(x*sqrt(ln(x)))dx# ? How do you find the integral #int_1^(3)12(1+5x)^5dx# ? How do you find the integral #int_0^(2)(10x)/sqrt(3-x^2)dx# ? How do you find the integral #int_0^1x^2*e^(x^3)dx# ? Question #23877 See all questions in Definite Integrals with Substitution Impact of this question 1833 views around the world You can reuse this answer Creative Commons License