Change of variable

Moving the red dot on the left with the mouse pointer selects a region under the curve y=sin2(x)cos(x). By the change of variable formula, the area of the region in blue on the left equals the area of the region in green under the curve y=u2 on the right. That is, with the change of variable u=sin(x), ∫a0sin2(x)cos(x)dx=∫sin(a)0u2du.




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