AP EAMCET · Maths · Definite Integration
\(\int_0^{400 \pi} \sqrt{1-\cos 2 x} d x=\)
- A \(100 \sqrt{2}\)
- B \(200 \sqrt{2}\)
- C \(400 \sqrt{2}\)
- D \(800 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(800 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\( \int_0^{400 \pi} \sqrt{1-\cos 2 x} d x = \int_0^{400 \pi} \sqrt{2 \sin^2 x} d x \) \( = \sqrt{2} \int_0^{400 \pi} |\sin x| d x = \sqrt{2} \times 400 \times \int_0^\pi \sin x d x \)…
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
- If \(-2, \frac{4}{3}, \frac{-4}{5}\) are the intercepts made by a plane on \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively then the direction cosines of a normal to this plane areAP EAMCET 2022 Easy
- The extreme values of \(4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)\) over \(R\), areAP EAMCET 2005 Medium
- Let \(A=\{1,2,3,4,5,6\}\) number of functions \(f\) from \(A\) to \(A\) such that \(f(m)+f(n)=7\), whenever \(m+n=7\) isAP EAMCET 2021 Hard
- Let \(f\) be a polynomial function defined on \([2,7]\). If \(f(2)=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7)\), then the maximum possible value attained by \(f\) at \(x=7\) isAP EAMCET 2019 Medium
- Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all four cards of the same suit isAP EAMCET 2022 Easy
- If \(\int \frac{3 x+1}{(x-1)^3(x+1)} d x=\mathrm{A} \cdot \log \left|\frac{x+1}{x-1}\right|+\frac{\mathrm{B}}{x-1}+\frac{\mathrm{C}}{(x-1)^2}+\mathrm{D}\) then \(\mathrm{A}+\mathrm{B}+\mathrm{C}=\)AP EAMCET 2018 Medium
More PYQs from AP EAMCET
- If \(I_n=\int \frac{\sin n x}{\cos x} d x\), then \(I_n=\)AP EAMCET 2017 Medium
- \[
\int_0^{50 \pi} \sqrt{1-\cos 2 x} d x=
\]AP EAMCET 2023 Hard - . A bullet of mass \(0.01 \mathrm{~kg}\) travelling at a speed of \(500 \mathrm{~ms}^{-1}\) strikes a block of mass \(2 \mathrm{~kg}\) which is suspended by a string of length \(5 \mathrm{~m}\). The centre of gravity of the block is found to rise a vertical distance of \(0.1 \mathrm{~m}\). What is the speed of the bullet after it emerges from the block?AP EAMCET 2020 Hard
- If eight coins are tossed simultaneously, then the probability of getting atleast six heads isAP EAMCET 2023 Medium
- If \(\cos \theta-\sin \theta=\sqrt{5} \sin \theta\), then \(\cos \theta+4 \sin \theta=\)AP EAMCET 2022 Medium
- An ac source of internal resistance \(10^3 \Omega\) is connected to a transformer. The ratio of the number of turns in the primary to the number of turns in the secondary to match the source to a load resistance of \(10 \Omega\) isAP EAMCET 2025 Medium