#### To determine

**To prove:**

the inequality ∫01xsin−1x dx≤π4.

#### Answer

We could prove the inequality ∫01xsin−1x dx≤π4

#### Explanation

**Given:**

∫01xsin−1x dx≤π4

**Formulae used:**

The relation of −π2≤sin−1x≤π2

Consider ∫01xsin−1x dx≤π4

Hence, use the formulae of −π2≤sin−1x≤π2

Now according to the given expression, the value of the given expression is

sin−1x≤π2∫01xsin−1x dx≤π2∫01xdx≤π4[x2]01≤π4

**Conclusion:** We could prove the inequality ∫01xsin−1x dx≤π4