# Integration problem

## Homework Statement

Evaluate the integral (upper limit x^3 and lower limit x) sin (t^2) dt

## The Attempt at a Solution

I tried using the second fundamental theorem to do: 3x^2 sin (x^6) - sin (x^2). I'm not sure if this is right though.

## Answers and Replies

Is it some kind of a double integral?

what do you mean by double integral?

You have to use Fresnel integrals. Integrating the sin(t^2) by hand is not easy. What class is this for?

It's AP Calculus AB.

That question shouldn't be there, are you sure you read the problem right? could it have been (sin(t))^2 instead?

The answer to the problem posted is as follows:

sqrt(Pi/2)[(S(sqrt(2/Pi)*x^3)-S(sqrt(2/Pi)*x)], where S(x) is the Fresnel integral of sin(t^2)dt from 0 to x.

I think they want the derivative not to evaluate the actual integral. Can I use the second fundamental theorem then?

Would you type in the instructions for the problem? I am not entirely sure what they are asking.

Dick
Science Advisor
Homework Helper
I think they want the derivative not to evaluate the actual integral. Can I use the second fundamental theorem then?

The question does ask for the derivative of that integral, yes? And yes, you can use a fundamental theorem. And yes, you did it correctly.

## Homework Statement

Evaluate the integral (upper limit x^3 and lower limit x) sin (t^2) dt

## The Attempt at a Solution

I tried using the second fundamental theorem to do: 3x^2 sin (x^6) - sin (x^2). I'm not sure if this is right though.

====

Yeah, I think that you are just over-complicating this...... what is the derivative of
y = (-1/(t^2))cos(t^2) .......

Okay, the derviative of that is the integrand of your problem.
evalulating y from the top and bottom (of the integral domain) yields:
(-1/x^6)cos(x^6) +(1/x^2)cos(x^2)

Dick
Science Advisor
Homework Helper
====

Yeah, I think that you are just over-complicating this...... what is the derivative of
y = (-1/(t^2))cos(t^2) .......

Okay, the derviative of that is the integrand of your problem.
evalulating y from the top and bottom (of the integral domain) yields:
(-1/x^6)cos(x^6) +(1/x^2)cos(x^2)

Wrong. The derivative of that is DEFINITELY not sin(t^2).