∫ (from 0 to pi) of (7sin(t)-9cos(t))dt-এর সমাধান করুন

$$\int _ { 0 } ^ { \pi } ( 7 \sin ( t ) - 9 \cos ( t ) ) d t$$

মূল্যায়ন করুন

$$14$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 7\sin(t)-9\cos(t)\mathrm{d}t$$

Integrate the sum term by term.

$$\int 7\sin(t)\mathrm{d}t+\int -9\cos(t)\mathrm{d}t$$

Factor out the constant in each of the terms.

$$7\int \sin(t)\mathrm{d}t-9\int \cos(t)\mathrm{d}t$$

Use \int \sin(t)\mathrm{d}t=-\cos(t) from the table of common integrals to obtain the result. 7 কে -\cos(t) বার গুণ করুন।

$$-7\cos(t)-9\int \cos(t)\mathrm{d}t$$

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

$$-7\cos(t)-9\sin(t)$$

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.

$$-7\cos(\pi )-9\sin(\pi )-\left(-7\cos(0)-9\sin(0)\right)$$

সিমপ্লিফাই।

$$14$$