How do you do this question?

0

Step-by-step explanation:

∫ sin²(x) cos(x) dx

If u = sin(x), then du = cos(x) dx.

∫ u² du

⅓ u³ + C

⅓ sin³(x) + C

Evaluate between x=0 and x=π.

⅓ sin³(π) − ⅓ sin³(0)

0

Step-by-step explanation:

So we have the integral:

To evaluate this integral, we can use u-substitution. Remember that the derivative of sin(x) is cos(x). So, let u equal sin(x):

Take the derivative of u:

Multiply both sides by dx:

So, we can substitute cos(x) x for du.

We can also substitute sin(x) for u. Thus:

So, our integral is now:

This is equal to:

However, we also must change our bounds of integration. To do so, substitute in the lower and upper bound into u. So:

And:

Therefore, our integral with our new bounds is:

Now, note that the integral has the same upper bound and lower bound. Therefore, this means that our integral is going to be 0 since with the same bounds, there will be no area.

Therefore, our answer is 0:

And we're done!

part a: 1.08

part b: 27.59

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.