Worked example
Evaluate the definite integral of 3x2 from x=0 to x=1.
Answer & why
Answer: 1
An antiderivative is × x3. Evaluate at 1 and 0: 3 × 13/3 = 1.
Grade 12 · Math
Integrate a quadratic over an interval
Evaluate a definite integral of a constant multiple of x².
8 authored questions + worked example
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All questions
All 8 authored questions for this skill.
Question 1
Evaluate the definite integral of 12x2 from x=0 to x=3.
- 108
- 110
- 109
- 107
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 108
An antiderivative is × x3. Evaluate at 3 and 0: 12 × 33/3 = 108.
Question 2
Evaluate the definite integral of 15x2 from x=0 to x=4.
- 322
- 319
- 320
- 321
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 320
An antiderivative is × x3. Evaluate at 4 and 0: 15 × 43/3 = 320.
Question 3
Evaluate the definite integral of 3x2 from x=0 to x=1.
- 1
- 0
- 2
- 3
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 1
An antiderivative is × x3. Evaluate at 1 and 0: 3 × 13/3 = 1.
Question 4
Evaluate the definite integral of 6x2 from x=0 to x=2.
- 16
- 15
- 17
- 18
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 16
An antiderivative is × x3. Evaluate at 2 and 0: 6 × 23/3 = 16.
Question 5
Evaluate the definite integral of 9x2 from x=0 to x=3.
- 80
- 82
- 83
- 81
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 81
An antiderivative is × x3. Evaluate at 3 and 0: 9 × 33/3 = 81.
Question 6
Evaluate the definite integral of 3x2 from x=0 to x=4.
- 64
- 66
- 65
- 63
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 64
An antiderivative is × x3. Evaluate at 4 and 0: 3 × 43/3 = 64.
Question 7
Evaluate the definite integral of 6x2 from x=0 to x=5.
- 250
- 252
- 251
- 249
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 250
An antiderivative is × x3. Evaluate at 5 and 0: 6 × 53/3 = 250.
Question 8
Evaluate the definite integral of 9x2 from x=0 to x=2.
- 24
- 25
- 23
- 26
A hint
Reverse the power rule, then subtract the lower-bound value from the upper-bound value.
Answer & why
Answer: 24
An antiderivative is × x3. Evaluate at 2 and 0: 9 × 23/3 = 24.