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Test: Integrals Of Special Functions - JEE MCQ


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5 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Integrals Of Special Functions

Test: Integrals Of Special Functions for JEE 2025 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Integrals Of Special Functions questions and answers have been prepared according to the JEE exam syllabus.The Test: Integrals Of Special Functions MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Integrals Of Special Functions below.
Solutions of Test: Integrals Of Special Functions questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Test: Integrals Of Special Functions solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Integrals Of Special Functions | 5 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
Test: Integrals Of Special Functions - Question 1
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Test: Integrals Of Special Functions - Question 2
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The value of 

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∫ [1 / (4x² - 12x + 25)] dx

First, factor out the coefficient of x² from the first two terms:

4x² - 12x + 25 = 4(x² - 3x) + 25

Next, complete the square for the expression inside the parentheses:

x² - 3x = (x - 1.5)² - 2.25

Substitute this back into the original expression:

4[(x - 1.5)² - 2.25] + 25 = 4(x - 1.5)² - 9 + 25 = 4(x - 1.5)² + 16

The integral now becomes:

∫ [1 / (4(x - 1.5)² + 16)] dx = (1/4) ∫ [1 / ((x - 1.5)² + 4)] dx
Recall the standard integral formula:

∫ [1 / (u² + a²)] du = (1/a) tan⁻¹(u/a) + C

In our case:

  • u = x - 1.5
  • a = 2

Applying the formula:

(1/4) * (1/2) tan⁻¹((x - 1.5)/2) + C = (1/8) tan⁻¹((2x - 3)/4) + C

The integral is:

∫ [1 / (4x² - 12x + 25)] dx = (1/8) tan⁻¹((2x - 3)/4) + C

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Test: Integrals Of Special Functions - Question 3
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Evaluate: 

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Test: Integrals Of Special Functions - Question 4
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The value of 

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Test: Integrals Of Special Functions - Question 5
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Evaluate: 

Detailed Solution for Test: Integrals Of Special Functions - Question 5

= tanx + cotx + C

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