Question

Integrate f(x) dx from 4 to 10 - integrate f(x) dx from 4 to 9 = integrate f(x) dx from a to b

Answer 1

Given:

`\int_4^(10)f(x)dx-\int_4^9f(x)dx=\int_a^bf(x)dx`

Required:

To find the value of a and b.

Step-by-step explanation:

Consider

`\begin{gathered} \begin{equation*} \int_4^(10)f(x)dx-\int_4^9f(x)dx \end{equation*} \\ \\ =\int_4^(10)f(x)dx-(-\int_9^4f(x)_dx) \\ \\ =\int_4^(10)f(x)dx+\int_9^4f(x)dx \\ \\ =\int_9^(10)f(x)dx \end{gathered}`

So the values of

`\begin{gathered} a=9 \\ b=10 \end{gathered}`

Final Answer:

`\begin{gathered} a=9 \\ b=10 \end{gathered}`