PUCET (Punjab) Integration by Parts — practice questions

Explore 2 free Integration by Parts questions in PUCET (Punjab) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integration by Parts questions and exercises with answers

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$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:Read the answer and worked solution →Fix the broken integral rulesRead the answer and worked solution →

Worked practice questions

$\int_1^2 \dfrac{\log x}{x^2}\,dx$ equals:

$(1 - \log 2)/2$
$\log 2 - 1$
$1 + \log 2$
$\log 2/2$

Show answer and solution

Correct answer: A. $(1 - \log 2)/2$

Integration by parts with $u = \log x$, $dv = dx/x^2$ gives $v = -1/x$: $[-\log x/x]_1^2 + \int_1^2 dx/x^2 = (-\log 2/2 - 0) + [-1/x]_1^2 = -\log 2/2 + (1 - 1/2) = (1 - \log 2)/2$.

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Fix the broken integral rules

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Questions

Statement parts
1. Swapping the two limits
2. of a definite integral
3. leaves its value
4. completely unchanged
Correction
flips its sign
Incorrect part
completely unchanged
Statement parts
1. An integral from a to a
2. always equals one
3. because that interval
4. has zero width
Correction
always equals zero
Incorrect part
always equals one
Statement parts
1. For an odd function
2. the integral from minus a to a
3. is twice the integral
4. from zero to a
Correction
is zero
Incorrect part
is twice the integral
Statement parts
1. An integral from a to b
2. may be split at c
3. whenever c lies
4. outside the two limits
Correction
between the two limits
Incorrect part
outside the two limits

Instructions

Every rule below has one piece stated wrongly. Tap the piece that does not belong.

_Source: Qallery verified question bank, MHT CET, topic Definite Integration_

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