∫ (from 0 to 1) of 2^x wrt x-এর সমাধান করুন

$$\int_{ 0 }^{ 1 } { 2 }^{ x } d x$$

মূল্যায়ন করুন

$$\frac{1}{\ln(2)}\approx 1.442695041$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 2^{x}\mathrm{d}x$$

Use \int x^{y}\mathrm{d}y=\frac{x^{y}}{\ln(x)} from the table of common integrals to obtain the result.

$$\frac{2^{x}}{\ln(2)}$$

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.

$$2^{1}\ln(2)^{-1}-2^{0}\ln(2)^{-1}$$

সিমপ্লিফাই।

$$\frac{1}{\ln(2)}$$