# How do you evaluate the definite integral #int (x+6)^2dx# from [0,4]?

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the definite integral ∫(x + 6)^2 dx from 0 to 4, you first expand the integrand, integrate the resulting polynomial function, and then apply the limits of integration. The steps are as follows:

- Expand the integrand: (x + 6)^2 = x^2 + 12x + 36.
- Integrate the expanded polynomial term by term: ∫(x^2 + 12x + 36) dx = (1/3)x^3 + 6x^2 + 36x + C.
- Evaluate the antiderivative at the upper and lower limits of integration: F(4) - F(0), where F(x) = (1/3)x^3 + 6x^2 + 36x.
- Substitute the upper limit: F(4) = (1/3)(4)^3 + 6(4)^2 + 36(4).
- Substitute the lower limit: F(0) = (1/3)(0)^3 + 6(0)^2 + 36(0).
- Subtract the value at the lower limit from the value at the upper limit: F(4) - F(0).

After performing these calculations, you will obtain the value of the definite integral ∫(x + 6)^2 dx from 0 to 4.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you evaluate #int sin(x^2)dx# from -1 to 2?
- How do you use the second fundamental theorem of Calculus to find the derivative of given #int 3/t^2 dt# from #[1,x]#?
- How do you use the second fundamental theorem of Calculus to find the derivative of given #int cos(t) / t dt # from #[3, x]#?
- How do you find the indefinite integral of #int (x(x+2))/(x^3+3x^2-4)#?
- How do you find the definite integral of #int 1/(xlnx)# from #[e,e^2]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7