# How do you solve #int_0^1 sqrt(5x+4) dx#?

We need to use a u-substitution to solve this question.

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To solve the integral ∫₀¹ √(5x + 4) dx, we can use the substitution method. Let u = 5x + 4. Then, du/dx = 5, or du = 5 dx. Solving for dx, we get dx = du/5.

Now, we substitute u = 5x + 4 and dx = du/5 into the integral:

∫₀¹ √(5x + 4) dx = ∫₄⁹ √u * (1/5) du

This simplifies to:

(1/5) ∫₄⁹ √u du

Now, we integrate √u with respect to u:

(1/5) * (2/3) * [u^(3/2)] from 4 to 9

Substituting the limits of integration:

(1/5) * (2/3) * [(9^(3/2)) - (4^(3/2))]

This further simplifies to:

(1/5) * (2/3) * [(27) - (8)]

And finally, evaluating:

(1/5) * (2/3) * [19]

= 38/15

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