### Evaluate the indefinite integral: ∫ 𝑒𝑥 √1 + 𝑒𝑥𝑑𝑥

Calculus

**10 calculus questions**

**Test 5 (Ch 5)****
**1. Express the limit as a definite integral on the given interval:

𝑙𝑖𝑚

𝑛→∞ ∑ 𝑥𝑖 𝑠𝑖𝑛 𝑥𝑖 Δ𝑥𝑛

𝑖=1 [0, 𝜋]

- Express the integral as a limit of the Riemann sums. Do not evaluate the limit:

∫ 𝑥

1 + 𝑥5 𝑑𝑥

8

1 - Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:

𝑔(𝑦) = ∫ 𝑡2 𝑠𝑖𝑛 𝑡

𝑦

2dt - Use Part 2 of the Fundamental Theorem of Calculus to evaluate the integral or explain why it does not exist:

∫ 𝑠𝑒𝑐2 𝑡

𝜋/4

0dt - Find the general indefinite integral: ∫(1 − 3𝑡)(5 + 𝑡2)𝑑𝑡
- Evaluate the integral:

∫ (10𝑥 + 𝑒𝑥)𝑑𝑥

0

−1 - Evaluate the indefinite integral:

∫ (𝑙𝑛 𝑥)

𝑥

3

𝑑𝑥 - Evaluate the indefinite integral: ∫ 𝑒𝑥 √1 + 𝑒𝑥𝑑𝑥
- Evaluate the definite integral, if it exists:

∫ (𝑥 − 1)9𝑑𝑥

2

0 - Find most general anti-derivative of the function:

𝑓(𝑢) = 𝑢4+𝑢√𝑢

𝑢2

Osman M

0

Tags :