Thread: Integration and Differentiation Problem

I took a math exam and want to see if I got these questions right. These are the ones I can remember.

3.) Integral of (sin x cos x) from x = -pi to x = pi.

We weren't allowed to ask questions so I didn't know if they wanted net area or all the area counted as positive, even the negative area so I put answer = 0.

6a.) Find dy/dx for the following equation of an hyperbola x^2 - y^2 = 9.

I got the answer dy/dx = -x/-y


6b.) What is the equation of the tangent line to the hyperbola at (3,0)

I put no such tangent line exists.

Originally Posted by Rstewart

3.) Integral of (sin x cos x) from x = -pi to x = pi.

We weren't allowed to ask questions so I didn't know if they wanted net area or all the area counted as positive, even the negative area so I put answer = 0.

This is an odd function. You should know that if is an odd function. So you are correct.

You could also have solved the integral using Brute Force.

Originally Posted by Rstewart

6a.) Find dy/dx for the following equation of an hyperbola x^2 - y^2 = 9.

I got the answer dy/dx = -x/-y


6b.) What is the equation of the tangent line to the hyperbola at (3,0)

I put no such tangent line exists.

I agree with the calculation of your derivative, though I would simplify it to x/y.

Anyway, for part b, what do you know about the gradients of vertical lines?

Originally Posted by Prove It

I agree with the calculation of your derivative, though I would simplify it to x/y.

Anyway, for part b, what do you know about the gradients of vertical lines?

>.< So that means it would be a vertical tangent and I got that one wrong?

Originally Posted by Rstewart

>.< So that means it would be a vertical tangent and I got that one wrong?

Yes, the equation of the tangent would have been .