How do you evaluate the definite integral #int (2)/(2x+5) * dx# from #[1, e]#?
Use substitution.
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the definite integral ∫(2)/(2x+5) dx from 1 to e:
- Find the antiderivative of the function (2)/(2x+5) with respect to x, which is ln|2x+5| + C.
- Evaluate the antiderivative at the upper limit of integration (e) and subtract the value of the antiderivative at the lower limit of integration (1).
- Substitute the upper limit (e) into the antiderivative: ln|2(e)+5| = ln|2e+5|.
- Substitute the lower limit (1) into the antiderivative: ln|2(1)+5| = ln|7|.
- Subtract the value at the lower limit from the value at the upper limit: ln|2e+5| - ln|7|.
- Simplify: ln| (2e+5) / 7 |. This is the value of the definite integral.
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.
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 find the integral of #int (dx / x^(2/3)) # from 1 to -15?
- What is the Integral of #tan^2(x)sec(x)#?
- How do you find the sum of the finite geometric sequence of #Sigma 2(-1/4)^n# from n=0 to 40?
- How do you evaluate the integral #int1/(1+x^2)^2 dx# from #-oo# to #oo#?
- How do you find the antiderivative of #f(x)=(2x^2-5x-3)/(x-3)#?

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