ECAT (Pre-Eng) Mathematics Chapter 19 Integration

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  A
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  C
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  D

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  D

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  A
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  D

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  A
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  D

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  A
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  B
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  D

The area between the x-axis and the curve y = x² + 1 from x = 1 to 2 is:

• 15/6 A
• 15/4 B
• 10/4 C
• 10/3 D

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  B
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  C
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  D

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  B
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  D

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  A
• In(x²- x + 1) + c B
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  C
• In(2x - 1) + c D

If the graph of f is entirely below the x-axis, then the value of definite integral is

• = 0 A
• < 0 B
• > 0 C
• None D

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  B
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  D

The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is

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  B
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  C
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  D

The general solution of the differential equation x dy / dx = 1 + y is:

• 2 A
• 1 B
• 3 C
• None D

• a sec(ax + b) + c A
• - a sec(ax + b) + c B
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  C
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  D

• 5x^{4 + c} A
• 1/6 x⁶+ c B
• 5x²+ c C
• 1/5 x⁶+ c D

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  B
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  D

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

• Differential equation A
• Initial condition B
• General solution C
• Singular equation D

∫Sec² (ax + b) dx is equal to:

• tan² (ax + b) A
• 1/a tan² (ax + b) B
• 1/atan (ax +b) C
• tan (ax + b) D

• Y = -x log x -x + c A
• Y = x log x + x B
• Y = x log x - x + c C
• None of these D

The function ø(x) is ananti derivativeof function f (x),x∈Df if

• ø′(x) =∫f(x)dx A
• ø(x) =∫f(x)dx B
• ø′(x) =f(x) C
• ø(x) =∫′(x)dx D

• a cos(ax + b) + c A
• - a cos(ax + b) + c B
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  C
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  D

Which of the following integrals can be evaluated

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  A
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  B
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  C
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  D

• 1 A
• 2 B
• 3 C
• 4 D

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  B
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  C
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  D

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  A
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  B
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  C
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  D

The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is

• 1.2% A
• 1.5% B
• 0.16% C
• 100.16% D

∫sin(ax+b) dx is equal to:

• 1/2a cos (ax + b) A
• -1/a cos (ax +b) B
• 1/a cos (ax +b) C
• 1/a ln (ax + b) D

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  A
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  B
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  C
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  D

• 2x - 3x + c A
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  B
• x²- 3x + c C
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  D

The area enclosed between the graph y = x² -4x and the x- axis is:

• 20/3 A
• 41/3 B
• 32/3 C
• 25/3 D