Question

1 ∫ | 5x-3 | dx ,Evaluate it. 0

Answer 1

Step-by-step explanation:

i hope this will help thnx

Answer 2

Answer:

This question will have two answers:-

$\frac{5x^{2}}{2} - 3x$

$\frac{-5x^{2}}{2} + 3x$

Step-by-step explanation:

In this question,

We have been asked,

To evaluate,  $\int{|5x-3|dx}$

Since|5x-3| can be written as  5x-3 and -5x+3

Therefore,

$\int{5x-3dx}\ =\ \int{5xdx}\ -\ \int{3dx}$

$\int{5x-3dx}\ =\ \frac{5x^{2}}{2}\ -\ 3x$            {Since,$\int{xdx}\ =\ \frac{x^{2}}{2}\ and\ \int{3dx}\ =\ 3x$}

Hence,

$\int{5x-3dx}\ =\ \frac{5x^{2}}{2}\ -\ 3x$

Similarly,

$\int{-5x+3dx}\ =\ \int{-5xdx}\ +\ \int{3dx}$

$\int{-5x+3dx}\ =\ \frac{-5x^{2}}{2}\ +\ 3x$         {Since,$\int{xdx}\ =\ \frac{x^{2}}{2}\ and\ \int{3dx}\ =\ 3x$}

Hence,

$\int{-5x+3dx}\ =\ \frac{-5x^{2}}{2}\ +\ 3x$