∫ (from 0 to 2) of left(-xright)^2+4 wrt x-এর সমাধান করুন

$$\int_{ 0 }^{ 2 } { \left(-x \right) }^{ 2 } +4 d x$$

মূল্যায়ন করুন

$$\frac{32}{3}\approx 10.666666667$$

সমাধানের ধাপগুলো

2 এর ঘাতে -x গণনা করুন এবং x^{2} পান।

$$\int _{0}^{2}x^{2}+4\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int x^{2}+4\mathrm{d}x$$

Integrate the sum term by term.

$$\int x^{2}\mathrm{d}x+\int 4\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{x^{3}}{3}+\int 4\mathrm{d}x$$

Find the integral of 4 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x^{3}}{3}+4x$$

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.

$$\frac{2^{3}}{3}+4\times 2-\left(\frac{0^{3}}{3}+4\times 0\right)$$

সিমপ্লিফাই।

$$\frac{32}{3}$$