CBSE-COMPARTMENT-XII SERIES

Mathematics

Indefinite Integrals

7 previous year questions.

Volume: 7 Ques

Yield: Medium

High-Yield Trend

1

2025

6

2023

Chapter Questions
7 MCQs

01

PYQ 2023

medium

mathematics ID: cbse-com

The value of is:

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4

02

PYQ 2023

medium

mathematics ID: cbse-com

$Find the area of triangle ABC bounded by: 5x -2y-10 =0, x-y-9=0, 3x-4y-6=0, usingintegrationmethod.$

Official Solution

Correct Option: (1)

$Question: Find the area bounded by the lines: 1. 2. 3. using the method of integration. Solution: Step 1: Convert the equations to slope-intercept form: Line 1: Line 2: Line 3: Step 2: Find the points of intersection: (i) Line 1 and Line 2: So, point (ii) Line 2 and Line 3: So, point (iii) Line 1 and Line 3: So, point Step 3: Set up integration to find area: Between and, the curves are: - Upper curve: - Lower curve: Area = Step 4: Integrate: Final Answer: Take absolute value:$

03

PYQ 2023

medium

mathematics ID: cbse-com

$Evaluate:$

Official Solution

Correct Option: (1)

$Step 1: Find breakpoints where expressions change sign: Step 2: - For : not needed. - For : So, - For : So, Therefore, Final Answer: 3$

04

PYQ 2023

medium

mathematics ID: cbse-com

$Find the integral:$

Official Solution

Correct Option: (1)

$Step 1: Use the identity Let, so Step 2: Rewrite the integral: Step 3: Complete the square in the denominator: Step 4: Now the integral becomes: This is of the standard form: Step 5: So, Substitute back : Final Answer:$

05

PYQ 2023

medium

mathematics ID: cbse-com

$Find:$

Official Solution

Correct Option: (1)

$Step 1: Use partial fractions: Multiply both sides by the denominator: Step 2: Expand the RHS: Group like terms: Step 3: Compare coefficients: Coefficient of : Coefficient of : Coefficient of : Constant term: From above: Step 4: So the decomposition becomes: Step 5: Now integrate: Step 6: Use standard integrals: So: Final Answer:$

06

PYQ 2023

medium

mathematics ID: cbse-com

$Evaluate:$

Official Solution

Correct Option: (1)

$Step 1: Use the substitution for definite integrals: Let’s check: But: So, So: Add: So, Combine numerator: So, Step 2: Substitute . So, So, Step 3: Expand denominator: So, Complete square: So, Step 4: Use formula: . Put : Therefore, Final Answer:$

07

PYQ 2025

medium

mathematics ID: cbse-com

$Evaluate the definite integral:$

Official Solution

Correct Option: (1)

$Let: Use substitution: Change limits: When When Final Answer:$

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