Find definite integral with variable

[Themrc]

I am having a devil of a time with this problem that involves finding the definite integral. I believe I need to use substitution but I'm not sure. I have the answer but I don't know how to get there so I need super detailed steps.

Please see the attached photo since I have no idea how to type out an integral symbol on iOS

 

[stapel]

I am having a devil of a time with this problem that involves finding the definite integral. I believe I need to use substitution but I'm not sure. I have the answer but I don't know how to get there so I need super detailed steps.

Please see the attached photo since I have no idea how to type out an integral symbol on iOS

To learn how to type math as text, try here:

. . . . .20) G(x) = int[0 to x] sqrt[4x + 3] dt

What, specifically, are your questions regarding this exercise?

 

[Themrc]

My question, specifically is that I need help solving the problem. I'm not asking for help writing math problems as text.

I've tried about 10 different ways to solve this problem and I never get the right answer. I need someone to solve the problem In very detailed steps. The answer is sqrt(4x+3)

 

[Themrc]

I need to know how to solve the problem, with detailed steps. That's my question. Sorry if I'm replying twice but I don't see my reply on the forum so I'm replying again.

 

[ksdhart]

The trick here is that you're differentiating with respect to t, rather than x. Since there is no t in the integral, all you have is a constant. What happens when you take the indefinite integral of that constant? And then if you evaluate the result over your given boundaries?

 

[Deleted member 4993]

The trick here is that you're differentiating with respect to t, rather than x. Since there is no t in the integral, all you have is a constant. What happens when you take the indefinite integral of that constant? And then if you evaluate the result over your given boundaries?

When you do that, You should get x*√(4x+3) - not the answer given.

 

[pka]

The trick here is that you're differentiating with respect to t, rather than x. Since there is no t in the integral, all you have is a constant. What happens when you take the indefinite integral of that constant? And then if you evaluate the result over your given boundaries?

This is the easiest question.
Suppose each of $\displaystyle \alpha~\&~\beta$ is a differentiable function and $\displaystyle F(x) =\displaystyle \int_{\alpha (x)}^{\beta (x)} {g(t)dt}$ THEN
$\displaystyle \large F'(x) = \beta '(x)g(\beta (x)) - \alpha '(x)g(\alpha (x))$.

 

[stapel]

I've tried about 10 different ways to solve this problem and I never get the right answer. I need someone to solve the problem In very detailed steps. The answer is sqrt(4x+3)

You already have loads of solved problem with "very detailed steps": check your textbook, your class notes, and any of the lessons you've viewed online. So one more worked example isn't going to help you find where things are going wrong.

On the other hand, once you've replied showing us what you've tried, we'll be well-placed to find specific errors so that you can get back on your way. So please do reply with that info; any one or more of the "about 10 different ways" you've so far "tried...to solve this problem will be great. Thank you!

 

[Steven G]

My question, specifically is that I need help solving the problem. I'm not asking for help writing math problems as text.

I've tried about 10 different ways to solve this problem and I never get the right answer. I need someone to solve the problem In very detailed steps. The answer is sqrt(4x+3)

No, the correct answer is xsqrt(4x+3)