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

$$\int _ { - 3 } ^ { 3 } 3 x ^ { 2 } d x$$

মূল্যায়ন করুন

$$54$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

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

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

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}. 3 কে \frac{x^{3}}{3} বার গুণ করুন।

$$x^{3}$$

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.

$$3^{3}-\left(-3\right)^{3}$$

সিমপ্লিফাই।

$$54$$