# 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)

1. 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 t-0, the f(lower)=0

t/sqrt(1-t^3) at t=x^3

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