Question

Please solve this.
I will mark brainliest.

Answer 1

Answer:

0

Step-by-step explanation:

Put x = 2a - u.

Then

• dx = -du
• x = a  <=>  u = a
• x = 2a  <=>  u = 0

Thus

$\displaystyle\int_a^{2a}f(x)\,dx\\\\=\int_a^0f(2a-u)(-du)\\\\=\int_0^af(2a-u)\,du\\\\=-\int_0^af(u)\,du\\=-\int_0^af(x)\,dx$

Therefore

$\displaystyle\int_0^{2a}f(x)\,dx\\\\=\int_0^af(x)\,dx + \int_a^{2a}f(x)\,dx\\\\=\int_0^af(x)\,dx - \int_0^af(x)\,dx\\\\=0$