Question

Encontre a antiderivada de:
a) dy/dx = x3 – 4
b) dy/dx = x4
c) dy/dx = 5x2 – 4x + 3

Answer 1

Resposta:

a) f ' = x⁴

b) f ' = 4x³

c) f ' = 10x - 4

Explicação passo-a-passo:

a) dy/dx = x³ – 4

f ' = x³ - 4 = 3x²

b) dy/dx = x⁴

f ' = x⁴ = 4x³

c) dy/dx = 5x2 – 4x + 3

f ' = 5x² - 4x + 3 = 10x - 4

Answer 2

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$\boxed{\begin{array}{l}\tt a)~\sf\dfrac{dy}{dx}=x^3-4\\\sf dy=(x^3-4)dx\\\displaystyle\sf\int dy=\int(x^3-4)dx\\\sf y(x)=\dfrac{1}{4}x^4-4x+k\\\tt b)~\sf\dfrac{dy}{dx}=x^4\\\sf dy=x^4~dx\\\displaystyle\sf\int dy=\int x^4~dx\\\sf y(x)=\dfrac{1}{5}x^5+k\\\tt c)~\sf\dfrac{dy}{dx}=5x^2-4x+3\\\sf dy=(5x^2-4x+3)~dx\\\displaystyle\sf\int dy=\int(5x^2-4x+3)~dx\\\sf y(x)=\dfrac{5}{3}x^3-2x^2+3x+k\end{array}}$