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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 29 June 2022, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

If ∫02(2x−2x−x2)dx=∫01(1−1−y2−y22)dy+∫12(2−y22)dy+I\int_0^2 \left(\sqrt{2x} - \sqrt{2x - x^2}\right) dx = \int_0^1 \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) dy + \int_1^2 \left(2 - \frac{y^2}{2}\right) dy + I then II equals
  1. (1)∫01(1+1−y2)dy\int_0^1 \left(1 + \sqrt{1 - y^2}\right) dy
  2. (2)∫01(y22−1−y2+1)dy\int_0^1 \left(\frac{y^2}{2} - \sqrt{1 - y^2} + 1\right) dy
  3. (3)∫01(1−1−y2)dy\int_0^1 \left(1 - \sqrt{1 - y^2}\right) dyOfficial answer
  4. (4)∫01(y22+1−y2+1)dy\int_0^1 \left(\frac{y^2}{2} + \sqrt{1 - y^2} + 1\right) dy

Official answer

Option 3

NTA final key.

Chapter
Application of Integrals
Topic
Area Under Curves
Idea tested
Optimal Strip Selection (dx vs dy)

Same topic in other shifts

All Area Under Curves questions
  1. 2 Apr 2026, Shift 2 · Q24If the area of the region bounded by 16x2−9y2=14416x^2 - 9y^2 = 144 and 8x−3y=248x - 3y = 24 is AA, then 3(A+6log⁡e(3))3(A + 6\log_e(3)) is equal toHardNumerical value
  2. 4 Apr 2026, Shift 1 · Q18The area of the region {(x,y):y≤π−∣x∣, y≤∣xsin⁡x∣, y≥0}\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\} is:HardSingle correct
  3. 4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves x+3y2=0x+3y^2=0 and x+4y2=1x+4y^2=1 is equal to:EasySingle correct
  4. 5 Apr 2026, Shift 1 · Q16The area of the region R={(x,y):xy≤27, 1≤y≤x2}R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\} is equal to:MediumSingle correct
  5. 5 Apr 2026, Shift 2 · Q24Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function such that f(x)+3f(π2−x)=sin⁡xf(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x, x∈Rx \in \mathbf{R}. Let the maximum…HardNumerical value
  6. 6 Apr 2026, Shift 1 · Q19The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\} is:MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.