JEE Main20249 Apr 2024Evening ShiftMathematicsDefinite IntegrationActual

Let ₀^x 1- (y^ (t) )^2 d t= ₀^x y(t) d t, 0 x 3, y 0, y(0)=0 . Then at x=2, y^ +y+1 is equal to

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A1
B2
C2
D1 / 2

Correct answer

A. 1

Step-by-step solution

aligned & 1- (y^ (x) )^2 =y(x) & 1- ( d y d x )^2=y^2 & ( d y d x )^2=1-y^2 aligned aligned & d y 1-y^2 =d x OR d y 1-y^2 =-d x & ⁻¹ y=x+c, ⁻¹ y=-x+c & x=0, y=0 c=0 & ⁻¹ y=x, as y 0 & x=y & d y d x = x & d^2 y d x^2 =- x & - x+ x+1=1 aligned

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