Integration
Math ⇒ Calculus
Integration starts at 11 and continues till grade 12.
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See sample questions for grade 12
Evaluate ∫ (2x + 5)3 dx using substitution.
Evaluate ∫ ex dx.
Evaluate ∫01 x3 dx.
Evaluate ∫0π/2 cos(x) dx.
Evaluate ∫0π sin(x) dx.
Evaluate ∫1e (1/x) dx.
If ∫14 f(x) dx = 9, what is ∫41 f(x) dx?
If ∫25 f(x) dx = 7 and ∫58 f(x) dx = 4, what is ∫28 f(x) dx?
The Fundamental Theorem of Calculus connects which two main concepts? (1) Differentiation and Integration (2) Limits and Derivatives (3) Sequences and Series (4) Functions and Graphs
Which of the following is NOT a method of integration? (1) Integration by substitution (2) Integration by parts (3) Integration by division (4) Integration by partial fractions
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 formula for the integration by parts? (1) ∫u dv = uv - ∫v du (2) ∫u dv = uv + ∫v du (3) ∫u dv = u/v - ∫v du (4) ∫u dv = uv - ∫u dv
If ∫ f(x) dx = F(x) + C, then d/dx [F(x)] = ________.
If F(x) is an antiderivative of f(x), then the general solution to ∫f(x) dx is ________.
If f(x) is an even function, then ∫-aa f(x) dx is equal to ________.
The antiderivative of sec2(x) is ________.
True or False: ∫aa f(x) dx = 0 for any continuous function f(x).
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.
True or False: The integral of a constant k with respect to x is kx + C.
True or False: The integral of an odd function over a symmetric interval [-a, a] is always zero.
