Question

| внизу 0 верху 2 e^x d x (вычисление интегралов) решите пожалуйста .

Answer 1

∫е×dx=e×I(предел от 0 до 2)=е²-е⁰=е²-1   Ответ  е²-1

Answer 2

Calculating the Integral of e^x + d*x

To solve the integral of e^x + d*x, we can break it down into two separate integrals: one for e^x and one for d*x. Let's solve each integral step by step.

# Integral of e^x

The integral of e^x can be found using the formula for the integral of a power of e:

∫ e^x dx = e^x + C

Here, C represents the constant of integration. So, the integral of e^x is simply e^x + C.

# Integral of d*x

The integral of d*x, where d is a constant, is straightforward:

∫ d*x dx = (d/2) * x^2 + C

Again, C represents the constant of integration.

# Combining the Integrals

To find the integral of e^x + d*x, we can add the integrals of e^x and d*x together:

∫ (e^x + d*x) dx = ∫ e^x dx + ∫ d*x dx

Substituting the integral formulas we derived earlier:

∫ (e^x + d*x) dx = (e^x + C1) + ((d/2) * x^2 + C2)

Here, C1 and C2 represent the constants of integration for each integral.

So, the solution to the integral of e^x + d*x is:

(e^x + C1) + ((d/2) * x^2 + C2)

Please note that the constants of integration, C1 and C2, can be any arbitrary constants.

I hope this explanation helps! Let me know if you have any further questions.