+95 Please help. Not very good at derviative of indefinite integrals
\(d/dx \int_{3}^{x} e^t cos(t^3) dt\)
\(d/dx \int_{x}^{3} e^t cos(t^3) dt\)
+776 1. \(e^t\cos{(t^3)},t\in{[\infty,3]}\)
2. \(e^t\cos{(t^3)},t\in{[3,-\infty]}\)
+33661 Essentially correct User101, though the result should be expressed in terms of x rather than t.
+33661 The dummy variable under the integral sign is t, but the integral itself is a function of x, and the derivative is taken with respect to x.
Imagine a simpler situation where you have d/dx of the integral from 0 to x of t with respect to t.
The integral would result in x^2/2, which, when differentiated wrt x would return x (not t).
