Integration and its Applications
CBSE · Class 12 · Applied Mathematics
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Quick Quiz: Integration and its Applications
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What is ∫(3x² + 2x - 1)dx?
Evaluate ∫₀² (x + 1)dx
Using substitution method, what is ∫2x(x² + 1)³dx?
What is ∫e^x dx?
Sample Questions
Which of the following are correct partial fraction decompositions? (Select all correct answers)
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1/((x-1)(x+2)) = A/(x-1) + B/(x+2), x/((x-1)²) = A/(x-1) + B/(x-1)², (x+1)/((x-2)(x+3)) = A/(x-2) + B/(x+3)
Options 1, 2, and 3 follow correct partial fraction rules. Option 4 is incorrect because x²+1 cannot be factored into linear factors with real coefficients.
Using integration by parts, what is ∫x·e^x dx?
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e^x(x-1) + C
Using ∫udv = uv - ∫vdu with u=x, dv=e^x dx: ∫xe^x dx = xe^x - ∫e^x dx = xe^x - e^x = e^x(x-1) + C.
Evaluate ∫₋₁¹ x³ dx
What is ∫1/x dx?
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log|x| + C
The integral of 1/x is log|x| + C. We use absolute value because x can be negative, and the logarithm of a negative number is undefined in real numbers.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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