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]
2. Express the integral as a limit of the Riemann sums. Do not evaluate the limit:
β« π₯
1 + π₯5 ππ₯
8
1
3. 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
4. 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
5. Find the general indefinite integral:
β«(1 β 3π‘)(5 + π‘2)ππ‘
6. Evaluate the integral:
β« (10π₯ + ππ₯)ππ₯
0
β1
7. Evaluate the indefinite integral:
β« (ππ π₯)
π₯
3
ππ₯
8. Evaluate the indefinite integral:
β« ππ₯ β1 + ππ₯ππ₯
9. Evaluate the definite integral, if it exists:
β« (π₯ β 1)9ππ₯
2
0
10. Find most general anti–derivative of the function:
π(π’) = π’4+π’βπ’
π’2