What is area y^2-27x=0,x+y=0 ?

The answer to area y^2-27x=0,x+y=0 is 243/2

area y^2-27x=0,x+y=0

area

y^{2} - 27 x = 0, x + y = 0

\frac{243}{2}

Decimal

121.5

Solution steps

Isolate

y

for

y^{2} - 27 x = 0 : y = 33 x, y = - 33 x

Isolate

y

for

x + y = 0 : y = - x

f_{1} (x) = 33 x

f_{2} (x) = - 33 x

To find the intersection points solve

f_{i} (x) = f_{j} (x)

33 x = - 33 x : x = 0

33 x = - x : x = 0

- 33 x = - x : x = 27, x = 0

= \int_{0}^{27} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{27} - 33 x - (- x) d x

\int_{0}^{27} - 33 x - (- x) d x = \frac{243}{2}

= \frac{243}{2}

t an g e n t f (x) = x^{3} + 4 x - 2, at x = 1

d er i v a t i v e 50 ln (2 x + 1) - \frac{x}{2}

\int_{5}^{\infty} \frac{2}{x ^{3}} d x

in v erse l a pl a ce \frac{5 s + 2}{( s + 1 ) ( s + 2 ) ^{2}}

\int - 10 x^{\frac{2}{3}} d x