Questions from General Calculus

Q: State the formula for 1h(x)dx for each of

State the formula for 1h(x)dx for each of the following functions. (a) h(x)xr, r ≠ -1 (b) h(x) = ekx (c) h(x) = 1/x (d) h(x) = f (x) + g(x) (e) h(x) = kf (x)

Q: Find the value of k that makes the antidifferentiation formula true.

Find the value of k that makes the antidifferentiation formula true. ∫2e4x-1 dx = ke4x-1 + C

Q: In the formula Δx = (b – a)/n,

In the formula Δx = (b – a)/n, what do a, b, n, and Δx denote?

Q: What is a Riemann sum?

What is a Riemann sum?

Q: Calculate the following integrals. ∫ 5√(x + 3

Calculate the following integrals. ∫ 5√(x + 3) dx

Q: Calculate the following integrals. ∫ e-x/2

Calculate the following integrals. ∫ e-x/2 dx

Q: Calculate the following integrals. ∫5/√(x – 7

Calculate the following integrals. ∫5/√(x – 7) dx

Q: Calculate the following integrals. ∫ (3x4 - 4x3)

Calculate the following integrals. ∫ (3x4 - 4x3) dx

Q: Calculate the following integrals. ∫ (2x + 3)

Calculate the following integrals. ∫ (2x + 3)7 dx

Q: Calculate the following integrals. ∫ √(4 – x)

Calculate the following integrals. ∫ √(4 – x) dx