The area of the region bounded between the curves y = e ∣ x ∣∣ ln ∣ x ∣∣ , x 2 + y 2 − 2 ( ∣ x ∣ + ∣ y ∣ ) + 1 ≥ 0 and x -axis where ∣ x ∣ ≤ 1 , if α is the x -coordinate of the point of intersection

Question

The area of the region bounded between the curves y = e ∣ x ∣∣ ln ∣ x ∣∣ , x 2 + y 2 − 2 ( ∣ x ∣ + ∣ y ∣ ) + 1 ≥ 0 and x -axis where ∣ x ∣ ≤ 1 , if α is the x -coordinate of the point of intersection of curves is 1st quadrant, is

TestHub · Accepted Answer

Required area is 2 [ ∫ 0 α ​ e x ln x d x + ∫ 1 α ​ ( 1 − 1 − ( x − 1 ) 2 ​ ) d x ] (shaded region in the graph), which on flipping the limits equals option (c).

Mathematics - Area Under Curves Question with Solution | TestHub

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