C ( x ) = ∫ (50+0.03x) wrt x-এর সমাধান করুন

$$C ( x ) = \int ( 50 + 0.03 x ) d x$$

মূল্যায়ন করুন

$$\frac{3x^{2}}{200}+50x+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int 50\mathrm{d}x+\int \frac{3x}{100}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 50\mathrm{d}x+\frac{3\int x\mathrm{d}x}{100}$$

Find the integral of 50 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$50x+\frac{3\int x\mathrm{d}x}{100}$$

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}. 0.03 কে \frac{x^{2}}{2} বার গুণ করুন।

$$50x+\frac{3x^{2}}{200}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$50x+\frac{3x^{2}}{200}+С$$

w.r.t. x পার্থক্য করুন

$$\frac{3x}{100}+50$$