Question

calcule a area entre as curvas f(x)=x^2-7 e f(x)=1-x^2

Answer 1

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$\int[1-x^2 - (x^2-7)]dx \\ \\ \int[-2x^2 + 8]dx \\ \\ - \frac{2 {x}^{3} }{3} + 8x + c$

$- \dfrac{2 {x}^{3} }{3} + 8x - ( - \dfrac{2 {x}^{3} }{3} + 8x) \\ \\ - \dfrac{2 {(2)}^{3} }{3} + 8(2)- ( - \dfrac{2 {( - 2)}^{3} }{3} + 8( - 2)) \\ \\ - \dfrac{16}{3} + 16- ( - \dfrac{ - 16}{3} - 16) \\ \\ - \dfrac{16}{3} + 16 - \dfrac{ 16}{3} + 16 \\ \\ - \dfrac{32}{3} + 32 \\ \\ \dfrac{ - 32 + 96}{3} \\ \\ \dfrac{64}{3}$

$\boxed{\boxed{A\approx 21,3 \: \: U.M ^2}}$