# Calculus homework help integrals

**Question description**

verify that F(x) is an antiderivative of the integrand f(x) and use Part 2 of the Fundamental Theorem to evaluate the definite integrals.

4. ⌡0 3⌠ (x^2 + 4x – 3 ) dx , F(x) = 1/3 x^3 + 2x^2 – 3x

6. Given A(x) = ⌡0 X⌠ 2t dt, find A'(x)

Find indicated antiderivative

1. t^5-t^2/t dt

2. e to 1] 1/x dx

3. 5 ~ 2 radical x dx

4. 1000 to 1 (1/x^2) dx

5. e^10/x / x^2 dx

6. 1 ~ 0 e^2x dx

7. 1 ~ 0 10x * e^3x dx

8. 2~1 ln(x)/ x^2 dx

9. Find the present and future values of a continuous income stream of $5000 per year for 12 years if money can earn 1.3% annual interest compounded continuously.10. Find the present value of a continuous income stream F(t) 20 += t , where t is in years and F is in tens of thousands of dollars per year, for 10 years, if money can earn 2% annual interest, compounded continuously.

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