Explanation
=(−2x33+x2)|10−∫xlogxdxto Integrate xlogxdx, substitute logx=t, dx=xdtIntegral becomes ∫e2ttdtIntegration by parts and then putting limits gives =−1/4
The ratio in which the area bounded by the curves y2=12x and x2=12y is divided by the line x = 3 is
y2=12x x2=12y ∫30√12x−∫30x212=∫30√12x−x212 2√12x323−x336∫30 √123√33−2736 12−34=454 Same as 84 for remaining part ∴ratio=1549
Locus of |z−(4+4i)|=4 is a circle with center at (4,4) and radius 4 is Complex plane.
Hence, locus of |z−(4+4i)|≥4 is all points either on or outside the circle with radius 4 and center (4,4).
Similarly, locus of |−z−(4+4i)|≥4 is all points on or outside the circle with radius 4 and center (−4,−4).
Locus of |iz−(4+4i)|≥4 is all points on or outside the circle with radius 4 and center (−4,4).
Finally, locus of |−iz−(4+4i)|≥4 is all points on or outside the circle with radius 4 and center (4,−4).
Hence, the area bounded by locus of all four will be the area enclosed by the four circles in argand plane as shown in the figure. Area bounded= area of shaded region=64−πr2=64−16π=16(4−π)
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