Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2013 · 23 April · Online · Mathematics · Area Under Curves

The area under the curve y=| x- x| , 0 ≤ x ≤ (π)/(2) , and above x...

The area under the curve y=∣cos⁡x−sin⁡x∣y=|\cos x-\sin x|, 0≤x≤π20 \leq x \leq \frac{\pi}{2}, and above xx-axis is :The area under the curve y=| x- x| , 0 ≤ x ≤ (π)/(2) , and above x -axis is :The area under the curve y=| x- x| , 0 ≤ x ≤ (π)/(2) , and above x -axis is :

Options

  1. A222 \sqrt{2}
  2. B22−22 \sqrt{2}-2
  3. C22+22 \sqrt{2}+2
  4. D0

Correct answer

B. 22−22 \sqrt{2}-2

Step-by-step solution

y=|\cos x-\sin x| <imgsrc="/api/proxy−image?url=https<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_main%252FatKCB74ZkroXBJdbLPn56sHqx0yarr6ySaTBFMpxDh4.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_main%2FatKCB74ZkroXBJdbLPn56sHqx0yarr6ySaTBFMpxDh4.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_main%2FatKCB74ZkroXBJdbLPn56sHqx0yarr6ySaTBFMpxDh4.original.fullsize.png?alt=media"> \\  Required area =2∫0π/4(cos⁡x−sin⁡x)dx=2[\sinx+cos⁡x00π/4]=2[22−1]=(22−2) sq. units \begin{aligned}\text{ Required area }& =2 \int_0^{\pi/ 4}(\cos x-\sin x) d x \\ & =2\left[\sinx+\cos x 0_0^{\pi/ 4}\right] \\ & =2\left[\frac{2}{\sqrt{2}}-1\right]=(2 \sqrt{2}-2) \text{ sq. units } \end{aligned}
Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If… JEE Advanced 2026The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is : JEE Main 2026The area of the region \ (x, y) : 0 ≤ y ≤ 6 - x, y^2 ≥ 4x - 3, x ≥ 0\ is: JEE Main 2026The area of the region R = \ (x, y): xy ≤ 27, 1 ≤ y ≤ x^2\ is equal to: JEE Main 2026The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to: JEE Main 2026The area of the region \ (x, y): y ≤ π - |x|, y ≤ |x x|, y ≥ 0\ is: JEE Main 2026If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A +… JEE Main 2026Let P_ 1 : y=4 x^ 2 and P_ 2 : y=x^ 2 +27 be two parabolas. If the area of the bounded… JEE Main 2026The area of the region R=\ (x, y): x y ≤ 8,1 ≤ y ≤ x^ 2 , x ≥ 0\ is JEE Main 2026Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^ 2 =x… JEE Main 2026Let A_ 1 be the bounded area enclosed by the curves y=x^ 2 +2, x+y=8 and y -axis that… JEE Main 2026The area of the region enclosed between the circles x^ 2 +y^ 2 =4 and x^ 2 +(y-2)^ 2 =4… JEE Main 2026Let the area of the region bounded by the curve y= \ x, x\ , lines x=0, x=(3 π)/(2) , and… JEE Main 2026The area of the region A=\ (x, y): 4 x^ 2 +y^ 2 8. and .y^ 2 4 x\ is: JEE Main 2026Let the line x=-1 divide the area of the region \ (x, y): 1+x^ 2 ≤ y ≤ 3-x\ in the ratio… JEE Main 2026 Full Area Under Curves list Area Under Curves JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs