What Is The Value Of The Definite Integral ∫₀¹ (2x + 1) Dx?

What is the value of the definite integral ∫₀¹ (2x + 1) dx?

Explanation

$\int_{01} (2 x + 1) d x$

Step 1: Integrate the function

We integrate each term separately:

$int (2x + 1), dx = int 2x, dx + int 1, dx = x^2 + x + C$

Step 2: Apply the limits from 0 to 1

$left[ x^2 + x right]_0^1 = (1^2 + 1) - (0^2 + 0) = 1 + 1 = 2$

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When x is multiplied by eight, it is increased by 5. Which equation represents this?

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Explanation

(x²+x−20)/(x²−4)

Step 1: Factorize the numerator and denominator.

x²+ x - 20 = (x + 5) (x - 4)

x²- 4 = (x - 2) (x + 2)

Step 2: Write the simplified expression.

(x+5)(x−4)/(x−2)(x+2)

If 54 is subtracted from 3 times a number, the result is 36. What is the number?

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What is the value of the definite integral ∫₀¹ (2x + 1) dx?

Explanation

Step 1: Integrate the function

Step 2: Apply the limits from 0 to 1

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What is the value of the definite integral ∫₀¹ (2x + 1) dx?

Explanation

Step 1: Integrate the function

Step 2: Apply the limits from 0 to 1

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