Q. 37 - Calculus

Question

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. 

$\int \pi dx$

Step-by-Step Solution

Answer

The solution of the integral is $\mathrm{\pi x}+\mathrm{C}.$

Step 1. Given Information.

The given integral is$\int \pi dx.$

Step 2. Solve.

By solving the integral we get, 

$$\begin{gathered} \int \mathrm{\pi dx} \\ =\mathrm{\pi }\int \mathrm{dx} \\ =\mathrm{\pi x}+\mathrm{C} \end{gathered}$$

Step 3. Verification.

To verify the answer we differentiate $\mathrm{\pi x}+\mathrm{C}$ it.

On differentiating we get,

$$\begin{gathered} \mathrm{\pi x}+\mathrm{C} \\ =\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{\pi x}+\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{C} \\ =\mathrm{\pi } \end{gathered}$$

Hence proved.