∫ (from 0 to pi) of 6sin(x) wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { \pi } 6 \sin ( x ) d x$$

মূল্যায়ন করুন

$$12$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 6\sin(x)\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$6\int \sin(x)\mathrm{d}x$$

Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.

$$-6\cos(x)$$

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.

$$-6\cos(\pi )+6\cos(0)$$

সিমপ্লিফাই।

$$12$$