Mathematics, 09.07.2019 07:30, abbasaliza01
Find the values of c such that the area of the region bounded by the parabola y = 16x2 − c2 and y = c2 − 16x2 is 250/3. (enter your answers as a comma-separated list.)
Answers: 1
![\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}](/tpl/images/0068/6050/e2f8e.png)
![So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68](/tpl/images/0068/6050/6f63b.png)
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Find the values of c such that the area of the region bounded by the parabola y = 16x2 − c2 and y =...
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