∫ (from - 1 to 1) of (4x^2-3) wrt x-এর সমাধান করুন

$$\int _ { - 1 } ^ { 1 } ( 4 x ^ { 2 } - 3 ) d x$$

মূল্যায়ন করুন

$$-\frac{10}{3}\approx -3.333333333$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

$$\int 4x^{2}-3\mathrm{d}x$$

Integrate the sum term by term.

$$\int 4x^{2}\mathrm{d}x+\int -3\mathrm{d}x$$

Factor out the constant in each of the terms.

$$4\int x^{2}\mathrm{d}x+\int -3\mathrm{d}x$$

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}. 4 কে \frac{x^{3}}{3} বার গুণ করুন।

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

Find the integral of -3 using the table of common integrals rule \int a\mathrm{d}x=ax.

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

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.

$$\frac{4}{3}\times 1^{3}-3-\left(\frac{4}{3}\left(-1\right)^{3}-3\left(-1\right)\right)$$

সিমপ্লিফাই।

$$-\frac{10}{3}$$