∫ (from 1 to sqrt { 2) of }f(x) wrt x-এর সমাধান করুন

$$\int _ { 1 } ^ { \sqrt { 2 } } f ( x ) d x$$

মূল্যায়ন করুন

$$\frac{f}{2}$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int fx\mathrm{d}x$$

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

$$f\int x\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.

$$f\times \frac{x^{2}}{2}$$

সিমপ্লিফাই।

$$\frac{fx^{2}}{2}$$

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.

$$\frac{1}{2}f\times \left(2^{\frac{1}{2}}\right)^{2}-\frac{1}{2}f\times 1^{2}$$

সিমপ্লিফাই।

$$\frac{f}{2}$$

w.r.t. f পার্থক্য করুন

$$\frac{1}{2} = 0.5$$