∫ (from 0 to 2) of a*x^3 wrt x-এর সমাধান করুন

$$\int _ { 0 } ^ { 2 } a \cdot x ^ { 3 } d x$$

মূল্যায়ন করুন

$$4a$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int ax^{3}\mathrm{d}x$$

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

$$a\int x^{3}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.

$$a\times \frac{x^{4}}{4}$$

সিমপ্লিফাই।

$$\frac{ax^{4}}{4}$$

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.

$$\frac{1}{4}a\times 2^{4}-\frac{1}{4}a\times 0^{4}$$

সিমপ্লিফাই।

$$4a$$

w.r.t. a পার্থক্য করুন

$$4$$