Write the integral in terms of u and du. Then evaluate: ∫(x-7)ˆ3dx, u=x-7
What is ∫uˆ3du=1/4(x-7)ˆ4+C
200
Calculate the integral: ∫(2xˆ3-1)ˆ2dx
What is 3/2xˆ4-3xˆ3+2xˆ2+C
300
L(5), f(x)= xˆ-1, [1,2]
What is L(5)≈ 0.745635
300
Calculate the integral of: ∫(-3,0) (2x-5)dx
What is -24
300
Evaluate ∫(-2,1) eˆxdx
What is e-(1/eˆ2)
300
Write the integral in terms of u and du. Then evaluate: ∫√(4x-1)dx, u=4x-1
What is 1/4∫uˆ1/2du=1/6(4x-1)ˆ3/2+C
300
Evaluate the definite integral: ∫(1,4) (x+(1/x))dx
What is 8.886 sq units
400
L(4), f(x)= cosx, [π/4, π/2]
What is L(4)≈0.328125
400
Calculate the integral of: ∫(0,4) eˆxdx
What is eˆ4-1
400
Evaluate the integral using FTC: ∫(1,4) (1/tˆ2)dt
What is 3/4
400
Evaluate the indefinite integral: ∫(4x+3)ˆ4dx
What is 1/20(4x+3)ˆ5+C
400
A chemical flows into a storage tank at a rate of 180+3t liters per minute, where 0≤t≤60. Find the amount of the chemical that flows into the tank during the first 20 minutes.
What is 4,200 liters of chemical flows into the tank each minute.
500
M(6), f(x)=lnx, [1,2]
What is M(6)≈ 0.386871
500
Calculate the integral of: ∫(-a,1) (xˆ2+x)dx
What is 1/3aˆ3-1/2aˆ2+5/6
500
Evaluate using FTC: ∫(-2,0) (3x-2eˆx)dx
What is 2eˆ-2-8
500
Use the Change of Variables Formula to evaluate the definite integral: ∫(-1,2) √(5x+6)dx
What is 42/5
500
A particle is moving along a line so that its velocity is v(t0=tˆ3-10tˆ2+29t-20 ft/sec at time t.
What is the displacement of the particle on the time interval 1≤t≤5?