Calculus
10 calculus questions
Test 5 (Ch 5)
1. Express the limit as a definite integral on the given interval:
πππ
πββ β π₯π π ππ π₯π Ξπ₯π
π=1 [0, π]
- Express the integral as a limit of the Riemann sums. Do not evaluate the limit:
β« π₯
1 + π₯5 ππ₯
8
1 - Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:
π(π¦) = β« π‘2 π ππ π‘
π¦
2dt - Use Part 2 of the Fundamental Theorem of Calculus to evaluate the integral or explain why it does not exist:
β« π ππ2 π‘
π/4
0dt - Find the general indefinite integral: β«(1 β 3π‘)(5 + π‘2)ππ‘
- Evaluate the integral:
β« (10π₯ + ππ₯)ππ₯
0
β1 - Evaluate the indefinite integral:
β« (ππ π₯)
π₯
3
ππ₯ - Evaluate the indefinite integral: β« ππ₯ β1 + ππ₯ππ₯
- Evaluate the definite integral, if it exists:
β« (π₯ β 1)9ππ₯
2
0 - Find most general anti-derivative of the function:
π(π’) = π’4+π’βπ’
π’2
