How do you do this problem?

Step-by-step explanation:

So we have the integral:

As told, let's use u-substitution first and then use integration by parts.

For the u-substitution, we can let u to be equal to x². So:

Differentiate:

We can rewrite our integral as:

Therefore, by making our u-substitution, our integral is now:

We also need to change our bounds. Substitute them into u. So:

Therefore, our integral with our new bounds is:

Now, let's use integration by parts. Integration by parts is given by:

(I changed the standard u to y because we are already using u).

Let's let v be 2u and let's let dy be cos(u). Thus:

And:

So, do integration by parts:

Simplify:

Evaluate the integral:

Now, use the bounds. So:

Evaluate:

Simplify:

Subtract:

And we're done!

we need the options

step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: