∫ (from x = 0 to pi / 2) of x wrt x-এর সমাধান করুন

$$\int _ { x = 0 } ^ { \pi / 2 } x d x$$

মূল্যায়ন করুন

$$\frac{\pi ^{2}}{8}\approx 1.23370055$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.

$$\frac{x^{2}}{2}$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\frac{1}{2}\times \left(\frac{1}{2}\pi \right)^{2}-\frac{0^{2}}{2}$$

সিমপ্লিফাই।

$$\frac{\pi ^{2}}{8}$$