Question

Which of the following inequalities is/are TRUE?

• A. $\int\limits_{0}^{1} x \cos x d x \geq \frac{3}{8}$
• B. $\int\limits_{0}^{1} x \sin x d x \geq \frac{3}{10}$
• C. $\int\limits_{0}^{1} x^{2} \cos x d x \geq \frac{1}{2}$
• D. $\int\limits_{0}^{1} x^{2} \sin x d x \geq \frac{2}{9}$

Answer 1

The Correct Option is A, B, D

(A) $\int\limits_{0}^{1} x \cos x d x \geq \frac{3}{8}$
(B) $\int\limits_{0}^{1} x \sin x d x \geq \frac{3}{10}$
(D) $\int\limits_{0}^{1} x^{2} \sin x d x \geq \frac{2}{9}$