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Test: Integration Basics - JEE MCQ


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7 Questions MCQ Test Physics for JEE Main & Advanced - Test: Integration Basics

Test: Integration Basics for JEE 2024 is part of Physics for JEE Main & Advanced preparation. The Test: Integration Basics questions and answers have been prepared according to the JEE exam syllabus.The Test: Integration Basics MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Integration Basics below.
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Test: Integration Basics - Question 1

Find ∫7 cos⁡mx dx.

Detailed Solution for Test: Integration Basics - Question 1

Step 1: Understand the Problem 

  • The problem is asking for the integral of the function 7cos(mx) with respect to x.

Step 2: Apply the Integral Rule

  • The integral of cos(mx) is (1/m)sin(mx).
  • Since there is a constant multiplier, 7, the constant can be factored out of the integral.

Step 3: Solve the Integral

  • Apply the integral rule to cos(mx) and multiply the result by the constant 7.

Step 4: Write the Final Answer

  • The integral of 7cos(mx) dx is 7*(1/m)sin(mx) + C, where C is the constant of integration.

Final Answer:

  • The integral ∫7cos(mx) dx = (7/m)sin(mx) + C
Test: Integration Basics - Question 2

Find ∫6x(x2+6)dx.

Detailed Solution for Test: Integration Basics - Question 2

The problem is asking to find the integral of 6x(x²+6)dx. This is a straightforward application of the power rule for integration.

Step 1:
First, distribute the 6x into the bracket.

• 6x * x² + 6x * 6 = 6x³ + 36x

Step 2:
Now, we can find the integral of each term separately.

• ∫6x³ dx + ∫36x dx

Step 3:
Apply the power rule for integration, which states that the integral of x^n dx is (1/n+1)x^(n+1).

• (6/4)x⁴ + (36/2)x² = 1.5x⁴ + 18x²

Step 4:
Finally, don't forget to add the constant of integration, denoted as 'c'.

Therefore, the integral of 6x(x²+6)dx is 1.5x⁴ + 18x² + c.

So, according to the options provided, the correct answer is Option C: f(x)+c.

Test: Integration Basics - Question 3

Integrate 3x2(cosx3+8).

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Test: Integration Basics - Question 4

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Test: Integration Basics - Question 5

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Test: Integration Basics - Question 6

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Test: Integration Basics - Question 7

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