Solveeit Logo
Login

Question

Mathematics Question on Methods of Integration

Which of the following inequalities is/are TRUE?

A

∫01xcos⁡xdx≥38\int\limits_{0}^{1} x \cos x d x \geq \frac{3}{8}

B

∫01xsin⁡xdx≥310\int\limits_{0}^{1} x \sin x d x \geq \frac{3}{10}

C

∫01x2cos⁡xdx≥12\int\limits_{0}^{1} x^{2} \cos x d x \geq \frac{1}{2}

D

∫01x2sin⁡xdx≥29\int\limits_{0}^{1} x^{2} \sin x d x \geq \frac{2}{9}

Answer

∫01xcos⁡xdx≥38\int\limits_{0}^{1} x \cos x d x \geq \frac{3}{8}

Explanation

Solution

(A) ∫01xcos⁡xdx≥38\int\limits_{0}^{1} x \cos x d x \geq \frac{3}{8}
(B) ∫01xsin⁡xdx≥310\int\limits_{0}^{1} x \sin x d x \geq \frac{3}{10}
(D) ∫01x2sin⁡xdx≥29\int\limits_{0}^{1} x^{2} \sin x d x \geq \frac{2}{9}