Question

If y=2x then value of int_(0)^(1)ydx is equal to​

Answer 1

Given:

y = 2x has been provided.

To find:

The integration?

Calculation:

$\displaystyle \: \int_{0}^{1} \: y \: dx$

$= \displaystyle \: \int_{0}^{1} \: 2x \: dx$

$= \displaystyle \: 2 \int_{0}^{1} \: x \: dx$

$= \displaystyle \: 2 \bigg \{\dfrac{{x}^{2}}{2} \bigg \}_{0}^{1}$

$= \displaystyle \: 2 \bigg \{\dfrac{ {1}^{2} - {0}^{2} }{2} \bigg \}$

$= \displaystyle 1$

So, value of definite integral is 1.