∫ (from 0 to 1) of 32x^7 wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { 1 } 32 x ^ { 7 } d x$$

মূল্যায়ন করুন

$$4$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 32x^{7}\mathrm{d}x$$

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

$$32\int x^{7}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{7}\mathrm{d}x with \frac{x^{8}}{8}. 32 কে \frac{x^{8}}{8} বার গুণ করুন।

$$4x^{8}$$

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.

$$4\times 1^{8}-4\times 0^{8}$$

সিমপ্লিফাই।

$$4$$