# How do you evaluate the definite integral #int (t^2+2)dt# from [-1,1]?

According to the power rule, we can just multiply our power by one and divide the resultant power so that

Within our bounds, subbing yields

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

To evaluate the definite integral ∫(t^2 + 2) dt from -1 to 1, you need to find the antiderivative of the integrand, which is (1/3)t^3 + 2t. Then, you evaluate this antiderivative at the upper limit (1) and subtract the value of the antiderivative at the lower limit (-1). So, the result is [(1/3)*(1)^3 + 2*(1)] - [(1/3)*(-1)^3 + 2*(-1)]. This simplifies to [(1/3) + 2] - [(1/3) - 2], which further simplifies to (1/3 + 2) - (1/3 - 2). Finally, this results in 7 - (-5/3), which equals 7 + 5/3, or 22/3. Therefore, the value of the definite integral is 22/3.

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 the definite integral #int 1+sinx # from #[0,pi]#?
- How do you evaluate the definite integral #int (-x^2+x+2)dx# from [-1,2]?
- Find the constant of integration #c# given that #f''(x)=2x# and the points #(1,0)# and #(0,5)# lie on the curve ?
- How do you integrate #int 1 / (sqrt(x+1) - sqrt(x)) #?
- How do you evaluate the integral #int 1/x dx# from 1 to #oo# if it converges?

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