AP calculus
posted by Anonymous .
∫[0,x^(3),(t)/√(1+t^(3)),]
Find the derivative of the integral.
A. (3(x^3))/((1+(x^9))^0.5)
B. (x^3)/((1+x^9)^0.5)
C. (3x^3)/((1+x^3)^0.5)
D. (5x^3)/((1+x^6)^0.5)
E. (3x^5)/((1+x^3)^0.5)
I think the answer is A. Can you check my answer please?

AP calculus 
bobpursley
derivative of an integral is the function.
consider a function f(t)
and then the integral from t=0 to a
int f(t) overlimits= INT f(t) at upperlimit int f(t) at lower limit
then d/dt INT f(t)= f(upper)f(lower).
so here, at t0, the f(lower)=0
and then the answer is
t/sqrt(1t^3) at t=x^3
answer B.
Respond to this Question
Similar Questions

calculus
Find the indefinite integral and check the result by differentiation. ∫3√((12x²)(4x))dx 
calculus
Find the indefinite integral and check the result by differentiation. ∫u²√(u^3+2) du 
Calculus
Find the integral by substitution ∫ [(16 x3)/(x4 + 5)] dx ∫[ 4 x/(√{x2 + 3})] dx ∫ 8 x2 e4 x3 +7 dx PLEASE help with all three. i'd really appreciate it 
Integral Calculus
Solve using Integration by Substitution : ∫√x2a2/x dx ∫√c2a dx ∫ ln (√y + 3) dy ∫(5y+4) dy/√5y1 
calculus
Evaluate the integral ∫∫∫2xzdV bounded by Q. Where Q is the region enclosed by the planes x + y + z = 4, y = 3x, x = 0, and z = 0. Answer=16/15 Is this answer correct? 
Calculus 2 correction
I just wanted to see if my answer if correct the integral is: ∫(7x^3 + 2x  3) / (x^2 + 2) when I do a polynomial division I get: ∫ 7x ((12x  3)/(x^2 + 2)) dx so then I use u = x^2 + 2 du = 2x dx 1/2 du = x dx = ∫7x … 
calculus (check my work please)
Not sure if it is right, I have check with the answer in the book and a few integral calculators but they seem to get a different answer ∫ sec^3(x)tan^3(x) dx ∫ sec^3(x)tan(x)(sec^2(x)1) dx ∫ tan(x)sec(x)[sec^4(x)sec^2(x)] … 
AP calculus
∫[0,x^(3),(t)/√(1+t^(3)),] Find the derivative of the integral. A. (3(x^3))/((1+(x^9))^0.5) B. (x^3)/((1+x^9)^0.5) C. (3x^3)/((1+x^3)^0.5) D. (5x^3)/((1+x^6)^0.5) E. (3x^5)/((1+x^3)^0.5) 
Calculus
Alright, I want to see if I understand the language of these two problems and their solutions. It asks: If F(x) = [given integrand], find the derivative F'(x). So is F(x) just our function, and F'(x) our antiderivative? 
Calculus
Which of the following integrals cannot be evaluated using a simple substitution?