What is area y= 1/2 x^2,y=-x^2+6 ?

The answer to area y= 1/2 x^2,y=-x^2+6 is 16

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area y= 1/2 x^2,y=-x^2+6

area

y = \frac{1}{2} x^{2}, y = - x^{2} + 6

16

Solution steps

Apply the area formula:

\int_{- 2}^{2} \frac{1}{2} x^{2} - (- x^{2} + 6) d x

Solve

\int_{- 2}^{2} \frac{1}{2} x^{2} - (- x^{2} + 6) d x : 16

The area is:

= 16

\int x \cdot ln (x - 1) d x

2 x \frac{d y}{d x} - y = 3 x^{2}

x \to 2 lim (\frac{1}{2 x})

\int 3 x^{2} e^{9 x^{3}} d x

f (x) = \frac{x - 1}{x + 3}