How do you find the definite integral of #int (2+3x-x^2) dx# from #[1,2]#?
It is
#int_1^2 (2+3x-x^2)dx=int_1^2 d/dx[2x+3/2x^2-x^3/3]dx= [2x+3/2x^2-x^3/3]_1^2=25/6#
By signing up, you agree to our Terms of Service and Privacy Policy
To find the definite integral of ( \int (2+3x-x^2) , dx ) from ( x = 1 ) to ( x = 2 ), you need to evaluate the antiderivative of the function at the upper limit of integration (2) and subtract the antiderivative at the lower limit of integration (1).
First, find the antiderivative of the function:
( \int (2+3x-x^2) , dx = 2x + \frac{3}{2}x^2 - \frac{1}{3}x^3 + C )
Now, evaluate the antiderivative at the upper and lower limits:
At ( x = 2 ): ( F(2) = 2(2) + \frac{3}{2}(2)^2 - \frac{1}{3}(2)^3 + C )
At ( x = 1 ): ( F(1) = 2(1) + \frac{3}{2}(1)^2 - \frac{1}{3}(1)^3 + C )
Subtract the value of the antiderivative at the lower limit from the value at the upper limit:
( \int_{1}^{2} (2+3x-x^2) , dx = [F(2) - F(1)] )
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.

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