Integration
Math ⇒ Calculus
Integration starts at 11 and continues till grade 12.
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See sample questions for grade 11
Evaluate ∫01 (4x + 1) dx.
Evaluate ∫02 (x2 + 2x) dx.
Evaluate ∫0π/2 cos(x) dx.
Evaluate ∫0π sin(x) dx.
If ∫13 f(x) dx = 5, what is ∫31 f(x) dx?
If ∫25 f(x) dx = 7 and ∫58 f(x) dx = 4, what is ∫28 f(x) dx?
If f(x) = 2x, what is the area under the curve from x = 0 to x = 3?
If f(x) = 4, what is ∫25 f(x) dx?
Which of the following is NOT a property of definite integrals?
(1) ∫ab f(x) dx = -∫ba f(x) dx
(2) ∫aa f(x) dx = 0
(3) ∫ab [f(x) + g(x)] dx = ∫ab f(x) dx + ∫ab g(x) dx
(4) ∫ab f(x) dx = ∫ab f(y) dy for any function f
Which of the following is the antiderivative of cos(x)?
(1) sin(x) + C
(2) -sin(x) + C
(3) cos(x) + C
(4) -cos(x) + C
Which of the following is the correct integral of 0 dx?
(1) 0
(2) C
(3) x + C
(4) 0 + C
Which of the following is the correct integral of 1/(1 + x2) dx?
(1) arctan(x) + C
(2) arcsin(x) + C
(3) ln|x| + C
(4) arccos(x) + C
If ∫ f(x) dx = F(x) + C, then F(x) is called the ________ of f(x).
If F(x) is an antiderivative of f(x), then ∫ab f(x) dx = ________.
If F(x) is an antiderivative of f(x), then d/dx [F(x)] = ________.
The constant of integration is denoted by the letter ________.
True or False: ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx for any c between a and b.
True or False: The area under the curve y = x2 from x = 0 to x = 1 is 1/3.
True or False: The definite integral can be negative.
True or False: The definite integral of a function from a to b gives the net area between the function and the x-axis from x = a to x = b.
