Question

Fill in the table by specifying the substitution you would choose to find each of the given integrals. Integral | Substitution u a. ? (2x + 5)??² dx b. ? te???² dt A) a. u = (2x + 5)??² B) a. u = 2x + 5 b. u = te???² b. u = 7 - t² C) a. u = 2x D) a. u = 2x b. u = t² b. u = 7 - t² Evaluate the given definite integral using the fundamental theorem of calculus. ??? (6 + 2t + 3t²) dt A) 68 B) -80 C) 40 D) 80 f(x) and g(x) are functions that are continuous on the interval -3 ? x ? 2 and satisfy ???² f(x) dx = 5, ???² g(x) dx = -2, ???¹ f(x) dx = 0, ???¹ g(x) dx = 4 Use this information along with rules for definite integrals to evaluate the indicated integral. ???² [4f(x) + 5g(x)] dx A) 10 B) 20 C) -10 D) 50 Solve the problem. Anita Bellman is a retailer who specializes in grains. She receives a shipment of 8000 kilograms of rice that will be used up over a 4-month period at the constant rate of 2000 kilograms per month. If storage costs are 90 cents per kilogram per month, how much will Anita pay in storage costs over the next 4 months? A) $16,000 B) $8100 C) $14,400 D) $1,440,000 Estimate the value of the definite integral ??? f(x) dx by computing the Riemann sum of f on the interval a ? x ? b for n = 8 subintervals, using left endpoints. Then find the actual value of the integral using the fundamental theorem of calculus. f(x) = 1/x over 3 ? x ? 5 A) 0.511; 0.528 B) 0.528; 0.511 C) 0.495; 0.511 D) 0.578; 0.511 The table gives the coordinates (x, f(x)) of points on the graph of a function f over the interval a ? x ? b. Estimate the value of the indicated definite integral ??? f(x) dx by forming a Riemann sum using left endpoints. ??² f(x) dx x | 0 | 0.4 | 0.8 | 1.2 | 1.6 | 2.0 f(x) | 1.3 | 1.6 | 1.9 | 2.3 | 2.1 | 1.8 A) 3.67 B) 11 C) 3.68 D) 9.2

          Fill in the table by specifying the substitution you would choose to find each of the given integrals.

Integral | Substitution u
a. ? (2x + 5)??² dx
b. ? te???² dt

A) a. u = (2x + 5)??² B) a. u = 2x + 5
b. u = te???² b. u = 7 - t²
C) a. u = 2x D) a. u = 2x
b. u = t² b. u = 7 - t²

Evaluate the given definite integral using the fundamental theorem of calculus.
??? (6 + 2t + 3t²) dt
A) 68 B) -80 C) 40 D) 80

f(x) and g(x) are functions that are continuous on the interval -3 ? x ? 2 and satisfy
???² f(x) dx = 5, ???² g(x) dx = -2, ???¹ f(x) dx = 0, ???¹ g(x) dx = 4
Use this information along with rules for definite integrals to evaluate the indicated integral.
???² [4f(x) + 5g(x)] dx
A) 10 B) 20 C) -10 D) 50

Solve the problem.
Anita Bellman is a retailer who specializes in grains. She receives a shipment of 8000 kilograms of rice that will be used up over a 4-month period at the constant rate of 2000 kilograms per month. If storage costs are 90 cents per kilogram per month, how much will Anita pay in storage costs over the next 4 months?
A) $16,000 B) $8100 C) $14,400 D) $1,440,000

Estimate the value of the definite integral ??? f(x) dx by computing the Riemann sum of f on the interval a ? x ? b for n = 8 subintervals, using left endpoints. Then find the actual value of the integral using the fundamental theorem of calculus.
f(x) = 1/x over 3 ? x ? 5
A) 0.511; 0.528 B) 0.528; 0.511 C) 0.495; 0.511 D) 0.578; 0.511

The table gives the coordinates (x, f(x)) of points on the graph of a function f over the interval a ? x ? b. Estimate the value of the indicated definite integral ??? f(x) dx by forming a Riemann sum using left endpoints.
??² f(x) dx
x | 0 | 0.4 | 0.8 | 1.2 | 1.6 | 2.0
f(x) | 1.3 | 1.6 | 1.9 | 2.3 | 2.1 | 1.8
A) 3.67 B) 11 C) 3.68 D) 9.2

Fill in the table by specifying the substitution you would choose to find each of the given integrals.

Integral | Substitution u
a. ? (2x + 5)??² dx
b. ? te???² dt

A) a. u = (2x + 5)??² B) a. u = 2x + 5
b. u = te???² b. u = 7 - t²
C) a. u = 2x D) a. u = 2x
b. u = t² b. u = 7 - t²

Evaluate the given definite integral using the fundamental theorem of calculus.
??? (6 + 2t + 3t²) dt
A) 68 B) -80 C) 40 D) 80

f(x) and g(x) are functions that are continuous on the interval -3 ? x ? 2 and satisfy
???² f(x) dx = 5, ???² g(x) dx = -2, ???¹ f(x) dx = 0, ???¹ g(x) dx = 4
Use this information along with rules for definite integrals to evaluate the indicated integral.
???² [4f(x) + 5g(x)] dx
A) 10 B) 20 C) -10 D) 50

Solve the problem.
Anita Bellman is a retailer who specializes in grains. She receives a shipment of 8000 kilograms of rice that will be used up over a 4-month period at the constant rate of 2000 kilograms per month. If storage costs are 90 cents per kilogram per month, how much will Anita pay in storage costs over the next 4 months?
A) 16,000 B)8100 C) 14,400 D)1,440,000

Estimate the value of the definite integral ??? f(x) dx by computing the Riemann sum of f on the interval a ? x ? b for n = 8 subintervals, using left endpoints. Then find the actual value of the integral using the fundamental theorem of calculus.
f(x) = 1/x over 3 ? x ? 5
A) 0.511; 0.528 B) 0.528; 0.511 C) 0.495; 0.511 D) 0.578; 0.511

The table gives the coordinates (x, f(x)) of points on the graph of a function f over the interval a ? x ? b. Estimate the value of the indicated definite integral ??? f(x) dx by forming a Riemann sum using left endpoints.
??² f(x) dx
x | 0 | 0.4 | 0.8 | 1.2 | 1.6 | 2.0
f(x) | 1.3 | 1.6 | 1.9 | 2.3 | 2.1 | 1.8
A) 3.67 B) 11 C) 3.68 D) 9.2

Added by Sofia T.

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