Verified answer

1/2 x² + 1/3 x^(3/2) + C

The integral of a * x^b = a * [1/(b+1)] x^(b + 1)

Prove it to yourself by differentiating this expression

I think the answer should be (2/3)x^(3/2) + (1/3)x^(3/2)

∫(√x + 1/2√x)dx

(2/3)x^3/2 + (2/3)(1/2)x^(3/2)+c

x^(3/2) +c

. . . . . .e area = ? ln x dx . . . . .a million . . . . . .. . . . . . . e area = -x + x ln x | . . . . . . . . . . . . . a million area = a million static 2d with admire to X axis, Sx = ? y dA Sx = ? y ((e - x) dy) Sx = ? y (e - e^y) dy . . . . a million Sx = ? y (e - e^y) dy . . . .0 . . . . . . . . . . . . . . . . . . a million Sx = ½ ey² - e^y (y - a million) | . . . . . . . . . . . , . . . . . . 0 Sx = ½ e - a million static 2d with admire to Y axis, Sy = ? x dA Sy = ? x (y dx) . . . . e Sy = ? x ln x dx . . . .a million . . . . . . . . . . . . . . . . .e Sy = ¼ x² (2 ln x - a million) | . . . .. . . . . . . . . . . . . a million Sy = ¼ (e² + a million) Xc = Sy/area = ¼ (e² + a million)/a million Xc = ¼ (e² + a million) Yc = Sx/area = (½ e - a million)/a million Yc = ½ e - a million coordinate of centroid is (Xc,Yc) = (¼ (e² + a million) , ½ e - a million)