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

$$\int_{ -1 }^{ 3 } 3x d x$$

মূল্যায়ন করুন

$$12$$

সমাধানের ধাপগুলো

Evaluate the indefinite integral first.

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

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

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

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}.

$$\frac{3x^{2}}{2}$$

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.

$$\frac{3}{2}\times 3^{2}-\frac{3}{2}\left(-1\right)^{2}$$

সিমপ্লিফাই।

$$12$$