Class 12 Maths MCQ – Properties of Definite Integrals

This set of Class 12 Maths Chapter 7 Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Definite Integrals”.

1. What is the difference property of definite integrals?
a) \(\int_a^b\)[-f(x)-g(x)dx
b) \(\int_a^b\)[f(-x)+g(x)dx
c) \(\int_a^b\)[f(x)-g(x)dx
d) \(\int_a^b\)[f(x)+g(x)dx
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2. The sum property of definite integrals is \(\int_a^b\)[f(x)+g(x)dx?
a) False
b) True
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3. What is the constant multiple property of definite integrals?
a) \(\int_a^b\)k⋅f(x)dy
b) \(\int_a^b\)[f(-x)+g(x)dx
c) \(\int_a^b\)k⋅f(x)dx
d) \(\int_a^b\)[f(x)+g(x)dx
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4. What is the reverse integral property of definite integrals?
a) –\(\int_a^b\)f(x)dx=-\(\int_b^a\)g(x)dx
b) –\(\int_a^b\)f(x)dx=-\(\int_b^a\)g(x)dx
c) \(\int_a^b\)f(x)dx=\(\int_b^a\)g(x)dx
d) \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx
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5. Identify the zero-length interval property.
a) \(\int_a^b\)f(x)dx = -1
b) \(\int_a^b\)f(x)dx = 1
c) \(\int_a^b\)f(x)dx = 0
d) \(\int_a^b\)f(x)dx = 0.1
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6. What is adding intervals property?
a) \(\int_a^c\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
b) \(\int_a^b\)f(x)dx+\(\int_b^a\)f(x)dx = \(\int_a^c\)f(x) dx
c) \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
d) \(\int_a^b\)f(x)dx-\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
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7. What is the name of the property of \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx?
a) Zero interval property
b) Adding intervals property
c) Adding integral property
d) Adding integrand property
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8. What is the name of the property \(\int_a^b\)f(x)dx=-\(\int_b^a\)f(x)dx?
a) Reverse integral property
b) Adding intervals property
c) Zero interval property
d) Adding integrand property
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9. What is the name of the property \(\int_a^b\)f(x)dx = 0?
a) Reverse integral property
b) Adding intervals property
c) Zero-length interval property
d) Adding integrand property
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10. What property this does this equation come under \(\int^1_{-1}\)sin⁡x dx=-\(\int_1^{-1}\)sin⁡x dx?
a) Reverse integral property
b) Adding intervals property
c) Zero-length interval property
d) Adding integrand property
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11. Evaluate \(\int_2^3\)3f(x)-g(x)dx, if \(\int_2^3\)f(x) = 4 and \(\int_2^3\)g(x)dx = 4.
a) 38
b) 12
c) 8
d) 7
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12. Compute \(\int_3^2\)f(x) dx if \(\int_2^3\)f(x) = 4.
a) – 4
b) 84
c) 2
d) – 8
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13. Compute \(\int_8^2\)2f(x)dx if \(\int_2^8\)f(x) = – 3.
a) – 4
b) 84
c) 2
d) – 8
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14. Compute \(\int_2^6\)7e^x dx.
a) 30.82
b) 7(e⁶ – e²)
c) 11.23
d) 81(e⁶ – e³)
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15. Evaluate \(\int_3^7\)2f(x)-g(x)dx, if \(\int_3^7\)f(x) = 4 and \(\int_3^7\)g(x)dx = 2.
a) 38
b) 12
c) 6
d) 7
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Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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