MHT CET · Maths · Definite Integration
\(\int_0^{\pi / 4} \sqrt{1-\sin 2 x} d x=\)
- A \(\sqrt{2}+1\)
- B \(1+2 \sqrt{2}\)
- C \(\sqrt{2}-1\)
- D \(2 \sqrt{2}-1\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2}-1\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\pi / 4} \sqrt{1-\sin 2 x} \mathrm{~d} x=\int_0^{\pi / 4}\) \(\sqrt{\cos ^2 x+\sin ^2 x-2 \sin x \cdot \cos x} \mathrm{~d} x \)
\( =\int_0^{\pi / 4} \sqrt{(\cos x-\sin x)^2} \mathrm{~d} x=\int_0^{\pi / 4}|\cos x-\sin x| \mathrm{d} x \)
\( =\int_0^{\pi / 4}(\cos x-\sin x) \mathrm{d} x=[\sin x+\cos x]_0^{\pi / 4} \)
\( =\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)-(0+1)=-1\)
\( =\int_0^{\pi / 4} \sqrt{(\cos x-\sin x)^2} \mathrm{~d} x=\int_0^{\pi / 4}|\cos x-\sin x| \mathrm{d} x \)
\( =\int_0^{\pi / 4}(\cos x-\sin x) \mathrm{d} x=[\sin x+\cos x]_0^{\pi / 4} \)
\( =\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)-(0+1)=-1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The solution of the differential equation \(\mathrm{e}^{\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)}=x+1 ; y(0)=5\), \(x \in(-1, \infty)\)MHT CET 2022 Easy
- Let \(f(x)=\frac{a x+b}{c x+d}\). Then, \(f o f(x)=x\) provided
thatMHT CET 2007 Easy - The logical expression
\([\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{r})]\) is equivalent toMHT CET 2020 Medium - A bag contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at most 2 of them are red isMHT CET 2022 Medium
- Let \(a, b, c\) and be non-zero real numbers, if the point of intersection of the lines \(4 a x+2 a y+c=0\) and \(5 b x+2 b y+d=0\) lies in the \(4^{\text {th }}\) quadrant and is equidistant from the two axes, thenMHT CET 2022 Easy
- Solution of \((2 y-x) \frac{d y}{d x}=1\) isMHT CET 2025 Medium
More PYQs from MHT CET
- In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series isMHT CET 2025 Medium
- Two springs have spring constant \(k_{A}\) and \(k_{B}\) and \(k_{A}>k_{B}\). The work required to stretch them by same extension will beMHT CET 2011 Easy
- A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing isMHT CET 2024 Medium
- If \(\mathrm{f}(\mathrm{x})=\frac{1}{\log \mathrm{x}}, \mathrm{g}(\mathrm{x})=\frac{1}{(\log \mathrm{x})^2}\)
(Where C is a constant of integration.)MHT CET 2022 Hard - Identify the reagent \(\mathrm{A}\) in the following conversion.
Alkyl halide \(\stackrel{\mathrm{A}}{\longrightarrow}\) Alkyl nitriteMHT CET 2023 Easy - Identify a side chain \((R)\) group present in Leucine, an amino acid.MHT CET 2025 Easy