# How do you solve #int_0^2 x^4+5x dx#?

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To solve the integral ∫₀²(x^4 + 5x) dx, you first need to integrate each term separately.

∫₀² x^4 dx = [x^5 / 5] from 0 to 2 = (2^5 / 5) - (0^5 / 5) = 32/5

∫₀² 5x dx = 5 * [x^2 / 2] from 0 to 2 = 5 * ((2^2 / 2) - (0^2 / 2)) = 5 * (2) = 10

Therefore, ∫₀²(x^4 + 5x) dx = 32/5 + 10 = 42/5.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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