15 Multiple Choice Calc

Question Description

1.

Evaluate the integral: the integral of the quantity x cubed over 4 plus 2 times x squared over 3 minus 1, dx (4 points)

x squared over 2 plus 4 times x over 3 minus 1 over x plus C

3 times x squared over 4 plus 4 times x over 3 minus 1 over x plus C

x4 + 2×3 – x + C

x to the 4th power over 16 plus 2 times x cubed over 9 minus x plus C

2.

Evaluate the integral of the quotient of the quantity x cubed minus x squared and x squared, dx . (4 points)

x – 1 + C

x squared over 2 minus x cubed over 3 plus C

the quotient of x to the 4th power minus x cubed and 4 times x squared plus C

x squared over 2 minus x plus C

3.

Evaluate the integral the integral of the quotient of the sine of x and the quantity 1 minus sine squared x, dx . (4 points)

2ln|1 – sin2(x)| + C

-csc(x) + C

sec(x) + C

None of these

4.

If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? (4 points)

the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a to b of g of x dx

the integral from a to a of f of x, dx equals 2 times the integral from 0 to a of f of x, dx

the integral from a to b of the product of f of x and g of x, dx equals the integral from a to b of f of x, dx times the integral from a to b of g of x dx

the integral from a to b of 3 plus f of x, dx equals 3 plus the integral from a to b of f of x, dx

5.

Evaluate the integral the integral of the cube root of x to the fifth power, dx . (4 points)

1 fifth times x raised to the 4 fifths power plus C

5 sixths times x raised to the 6 fifths power plus C

5 halves times x raised to the 3 halves power plus C

2 sevenths times x raised to the 7 halves power plus C

1.

Evaluate the integral the integral of the product of x cubed and the 5th power of x to the fourth plus 1, dx . (4 points)

the product of 1 over 6 and the 6th power of x to the fourth power plus 1 plus C

the product of x cubed over 18 and the 6th power of x to the fourth power plus 1 plus C

the product of 1 over 24 and the 6th power of x to the fourth power plus 1 plus C

the product of x to the fourth over 4 and the 5th power of x to the 5th power over 5 plus x plus C

2.

Evaluate the integral the integral of cosecant squared of 5 times x, dx . (4 points)

-2csc(5x)cot(5x) + C

-10csc(5x)cot(5x) + C

negative one fifth times the cotangent of 5 times x plus C

one over 15 times the cosecant cubed of 5 times x plus C

3.

Which of the following integrals cannot be evaluated using a simple substitution? (4 points)

the integral of 1 divided by the quantity x to the fourth power plus 1, dx

the integral of 1 divided by the quantity x squared plus 1, dx

the integral of x divided by the quantity x squared plus 1, dx

the integral of x cubed divided by the quantity x to the 4th power plus 1, dx

4.

Evaluate the integral of the quotient of 3 times x squared and the square root of 1 minus x cubed, dx . (4 points)

negative 1 times the natural logarithm of the square root of 1 minus x cubed, plus C

-ln|1 – x3| + C

sin-1(x3) + C

negative 2 times the natural logarithm of the square root of 1 minus x cubed, plus C

5.

Evaluate the integral the integral of the quotient of x squared and the quantity x plus 1, dx . (4 points)

x squared over 2 minus x minus 3 halves plus the natural logarithm of x plus 1, plus C

x cubed over 3 times the natural logarithm of x plus 1, plus C

x – 1 + ln|x| + C

x cubed divided by the quantity 3 times x plus 3, plus C

1.

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? (4 points)

the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx

the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx

the integral from 0 to 2 of the quantity 1 minus x squared, dx

2 times the integral from 0 to 1 of the quantity 1 minus x squared, dx

2.

Suppose the integral from 2 to 8 of g of x, dx equals 5 , and the integral from 6 to 8 of g of x, dx equals negative 3 , find the value of the integral from 2 to 6 of 2 times g of x, dx . (4 points)

8

12

16

4

3.

Evaluate the integral the integral from negative 1 to 1 of the absolute value of x, dx . (4 points)

1

0

2

-1

4.

Use your graphing calculator to evaluate to three decimal places the value of the integral negative 2 to 0 of the product x squared and the square root of x cubed over 8 plus 1, dx . (4 points)

0.250

2.667

1.778

-3.251

5.

the integral from 2 to 3 of 1 divided by the quantity 3 times x minus 2, dx is equal to the integral from 4 to 7 of 1 divided by u, du (4 points)

True

False

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