MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2024: question 24(a)

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerIntegrals

Find : $\int cos^{3} x e^{l o g s i n x} d x$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

$e^{l o g u} = u$ .

Hint 2

After simplifying, substitute $t = cos x$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Since $e^{l o g s i n x} = sin x$ , $I = \int cos^{3} x sin x d x$ . Put $cos x = t \Rightarrow - sin x d x = d t$ .
1 mark
$I = - \int t^{3} d t = - \frac{t ^{4}}{4} + C$
½ mark
$= - \frac{c o s ^{4} x}{4} + C$
½ mark

Answer: $- \frac{c o s ^{4} x}{4} + C$

Where the marks are

Simplifies $e^{l o g s i n x} = sin x$ and substitutes $cos x = t$ (1 mark)
Integrates $- \int t^{3} d t$ (½ mark)
Writes answer in terms of x (½ mark)

Revise the chapter

Chapter: Integrals (notes, formulas, where marks are lost and every past question)
Topic: Integration by Substitution

Practise this chapterBoard-style questions from Integrals, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2024: question 24(a)

Hints

Step-by-step solution

Revise the chapter

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