- #1
mnaeem
- 2
- 0
what is
d/dx of INT[ exp(-x^2/2*sin(t)^2) dt ] from 0 to pi/2
d/dx of INT[ exp(-x^2/2*sin(t)^2) dt ] from 0 to pi/2
mnaeem said:d/dx of INT[ exp(-x^2/2*sin(t)^2) dt ] from 0 to pi/2
ZioX said:That's not a definite integral. It has an x in it, hence it will be a function of x.
The derivative of an integral is the original function from which the integral was derived. It represents the rate of change of the integral with respect to the variable of integration.
To find the derivative of an integral, you can use the Fundamental Theorem of Calculus, which states that the derivative of an integral is equal to the integrand evaluated at the upper limit of integration.
The derivative of an integral helps to understand the relationship between a function and its integral. It also helps in solving problems related to rates of change and optimization.
Yes, the derivative of an integral can be negative if the function being integrated is decreasing over the interval of integration.
Yes, the derivative of an integral can be a constant if the function being integrated is a linear function or a constant function.