∫ (from 1 to 2) of 3/t^4dt-এর সমাধান করুন

$$\int _ { 1 } ^ { 2 } \frac { 3 } { t ^ { 4 } } d t$$

মূল্যায়ন করুন

$$\frac{7}{8}=0.875$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int \frac{3}{t^{4}}\mathrm{d}t$$

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

$$3\int \frac{1}{t^{4}}\mathrm{d}t$$

Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{t^{4}}\mathrm{d}t with -\frac{1}{3t^{3}}. 3 কে -\frac{1}{3t^{3}} বার গুণ করুন।

$$-\frac{1}{t^{3}}$$

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.

$$-2^{-3}+1^{-3}$$

সিমপ্লিফাই।

$$\frac{7}{8}$$