Question

Solve the attachment...​

Answer 1

Explanation:

=
`\int\limits^1_0 {5x√(x) } \, dx`

=
`\int\limits^1_0 {5xx^(1/2) } \, dx`

=
`\int\limits^1_0 {5x^(3/2) } \, dx`

= 5
`\int\limits^1_0 {x^(3/2) } \, dx`

= 5*
`(2)/(5)`*
`x^(5/2)` |
`\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left`

= 5*
`(2)/(5)`*
`1^(5/2)`

= 2

Answer 2

2 ( Option A )

Explanation:

The given integral to us is ,

`\longrightarrow \displaystyle \int_0^1 5x √(x)\ dx`

Here 5 is a constant so it can come out . So that,

`\longrightarrow \displaystyle I = 5 \int_0^1 x √(x)\ dx`

Now we can write √x as ,

`\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{(1)/(2)} \ dx`

Simplify ,

`\longrightarrow I = 5 \displaystyle \int_0^1 x^{(3)/(2)}\ dx`

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

`\longrightarrow I = 5 \bigg( (2)/(5) x^{(5)/(2)} \bigg] ^1_0 \bigg)`

On simplifying we will get ,

`\longrightarrow \underline{\underline{ I = 2 }}`