Calculus-definite integrals applications

Multiple Choice

Find g(2)

• -1/2
• -1
• 1
• 1/2

Multiple Choice

Given that $$∫_2^5g(x)dx=-7$$  and   $$\int_5^9\ g\left(x\right)dx=10$$  

Find  the value of   $$∫_2^9g(x)dx$$         

• -17

• 3

• -3

• 17

Multiple Choice

• ⅝
• -⅝
• ⅜
• 45/16

Multiple Choice

∫_₀^²(3x² - 2x)dx ?

• 8

• 4

• -8

• -4

Multiple Choice

A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t². If the particle is at position p=7 at t=1, what is the position of the particle at t=2?

• -10

• -5

• -3

• 3

Multiple Choice

Evaluate the definite integral.

• 3

• 9/2

• 9

• -9/2

Multiple Choice

Find the area of the shaded region.

• -7/3

• -13/3

• 13/3

• 7/3

Multiple Choice

Find the area under the curve y =3x²-2x from x= 1 to x =5.

• 100

• 99

• 150

• 152

Multiple Choice

Using the areas of each region given
$$\int_a^df\left(x\right)=$$  

• 6

• 20

• 2

• 24

Multiple Choice

Evaluate in terms of area

∫₀² f(x) dx

• 4

• -4

• 4 + 2π

• -4 - 2π

Multiple Choice

Evaluate in terms of area

∫₀¹⁴ f(x) dx

• 10π + 4

• 8π - 4

• 6π + 4

• 6π - 4

Multiple Choice

If oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does ∫₀¹²⁰r(t) dt represent?

• The total amount of oil that has leaked out in gallons in 120 minutes.

• The total rate that the oil has leaked out in gallons per minute over 120 minutes.

• The total time in minutes that the oil leaked out.

• The average amount of oil that has leaked out in gallons over 120 minutes.

Multiple Choice

The function v(t) = 2t - 6 is the velocity in m/sec of a particle moving along the x-axis, where t is measured in seconds. Find the total distance traveled by the particle for 0 ≤ t ≤ 5.

• -5 m

• 23 m

• 13 m

• 5/3 m

Multiple Choice

• A

• B

• C

• D

• E