Question

The area bounded by y = `sinx/x`, X-axis and the ordinates x = 0, x = π / 4 is ______.

Options

• equal to π / 4

• smaller π / 4

• greater π / 4

• smaller `int_0^(π//4) tanx/x dx`

Answer 1

The area bounded by y = `sinx/x`, X-axis and the ordinates x = 0, x = π / 4 is smaller π / 4.

Explanation:

We have, x > 0

∴ sin x < x

`\implies sinx/x < 1`

`\implies int_0^(π//4) sinx/x dx < int_0^(π//4) 1 dx = π/4`

or `int_0^(π//4) sinx/x dx < π/4`