Given Vallias' value for ∫0ax2dx,calculate his value for ∫0axdx, using graph.

Solved: "Given Vallias' value for ∫0ax2dx,calculate his value for..."

ediculeN

Answered question

2020-11-12

Given Vallias' value for

\int_{0}^{\sqrt{a}} x^{2} d x

,
calculate his value for

\int_{0}^{a} \sqrt{x} d x,

using graph.

Answer & Explanation

oppturf

Skilled2020-11-13Added 94 answers

Step 1
Let's look at this picture and look at the regions

Step 2
From the above figure, it is observed that length and breadth of the rectangle are a and square root of a. the area of rectangle can be given as follows.
Area of the $= \int_{0}^{\sqrt{a}} x^{2} d x + \int_{0}^{a} \sqrt{x} d x$
$l e n g t h \times b r e a d t h = \int_{0}^{\sqrt{a}} x^{2} d x + \int_{0}^{a} \sqrt{x} d x$
$a \times \sqrt{a} = \int_{0}^{\sqrt{a}} x^{2} d x + \int_{0}^{a} \sqrt{x} d x$
$\int_{0}^{a} \sqrt{x} d x = a \sqrt{a} - \int_{0}^{\sqrt{a}} x^{2} d x$
Thus, for given Wallis's value for $\int_{0}^{\sqrt{a}} x^{2} d x$ , it be obtained that
$\int_{0}^{a} \sqrt{x} d x = a \sqrt{a} - \int_{0}^{\sqrt{a}} x^{2} d x$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Didn't find what you were looking for?