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10 cards from this deck
∫x1x2y dx\int_{x_1}^{x_2} y \, dx∫x1x2ydx
∫y1y2x dy\int_{y_1}^{y_2} x \, dy∫y1y2xdy
y=4y=4y=4 when x=2x=2x=2 in y=x2y=x^2y=x2.
∫416y12 dy\int_4^{16} y^{\frac{1}{2}} \, dy∫416y21dy
Expand, integrate each term, and add constant of integration.
Integrate the top curve minus the bottom curve.
Integrate 6x3/26x^{3/2}6x3/2 from valid limits to find area.
Integrate ∫128x2−2 dx\int_1^2 \frac{8}{x^2}-2 \, dx∫12x28−2dx.
Total area = 125+2=225\frac{12}{5} + 2 = \frac{22}{5}512+2=522.
It links differentiation and integration through antiderivatives.
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