How do you differentiate #G(x) = intsqrtt sint dt# from #sqrt(x)# to #x^3#? Calculus Introduction to Integration The Fundamental Theorem of Calculus 1 Answer Konstantinos Michailidis Sep 8, 2015 You have #G(x)=int_sqrt(x)^(x^3)sqrt(t)*sintdt=>d(G(x))/dx=sqrt(x^3)*sin(x^3)*(3x^2)-sqrt(sqrt(x))*sin(sqrt(x))*(1/(2*sqrt(x)))# Answer link Related questions What is the Fundamental Theorem of Calculus for integrals? How does the fundamental theorem of calculus connect derivatives and integrals? How do you use the Fundamental Theorem of Calculus to evaluate an integral? How do you evaluate the integral #int_0^1x^2dx# ? How do you evaluate the integral #int_0^(pi/4)cos(x)dx# ? How do you evaluate the integral #int_1^(4)1/xdx# ? How do you use the Fundamental Theorem of Calculus to find the derivative of... How do you solve the AP Calculus 2013 Free Response question... How do you use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the... How do you use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the... See all questions in The Fundamental Theorem of Calculus Impact of this question 4031 views around the world You can reuse this answer Creative Commons License