Calculate the shaded area as given below : Option 1: 8/3 sq. units Option 2: 8/5 sq. units Option 3: 3 sq. units Option 4: 8 sq. units

Answer: 8/3 sq. units. Solution: Triangle with vertices (-2,0),(2,2),(2,-2) has area 1/2* 4* 4=8. Area inside parabola y^2=2x from x=0 to x=2: 2_0^2√2x dx=2√22/3 2√2=16/3. Shaded area =8-16/3=8/3 sq. units.

Calculus

Application of Integrals

Hard

core

Calculate the shaded area as given below :

$\frac{8}{3}$ sq. units

$\frac{8}{5}$ sq. units

3 sq. units

8 sq. units

✅ Correct Option: 1

Triangle with vertices $(-2,0),(2,2),(2,-2)$ has area $\frac{1}{2}\cdot 4\cdot 4=8$ .

Area inside parabola $y^2=2x$ from $x=0$ to $x=2$ :

$2\int_0^2\sqrt{2x}\,dx=2\sqrt{2}\cdot\frac{2}{3}\cdot 2\sqrt{2}=\frac{16}{3}$ .

Shaded area $=8-\frac{16}{3}=\frac{8}{3}$ sq. units.

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Calculate the shaded area as given below :

Solution

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