Find the total area of the region between the curve and the x-axis.
-$$\mathrm { y } = \frac { 1 } { \sqrt { \mathrm { x } } } ; 1 \leq \mathrm { x } \leq 4$$
A) 2
B) 4
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The area under the curve $y = \frac{1}{\sqrt{x}}$ from $x = 1$ to $x = 4$ can be found by integrating the function with respect to $x$ over the given interval. The integral of $y = \frac{1}{\sqrt{x}} = x^{-\frac{1}{2}}$ from 1 to 4 is $\int_{1}^{4} x^{-\frac{1}{2}} dx = [2x^{\frac{1}{2}}]_{1}^{4} = 2(4^{\frac{1}{2}}) - 2(1^{\frac{1}{2}}) = 2(2) - 2(1) = 4 - 2 = 2$.

Find the Total Area of the Region Between the Curve y=1x;1≤x≤4\mathrm { y } = \frac { 1 } { \sqrt { \mathrm { x } } } ; 1 \leq \mathrm { x } \leq 4y=x​1​;1≤x≤4

Find the Total Area of the Region Between the Curve $\mathrm { y } = \frac { 1 } { \sqrt { \mathrm { x } } } ; 1 \leq \mathrm { x } \leq 4$