Antiderivatives of Functions with Radicals | math4u.vsb.cz

Submitted by michaela.bailova on Wed, 09/25/2024 - 14:26

Project ID:

7200020150

Accepted:

SubArea:

Primitive function

Type:

Layout:

Question:

Pair the function

f

with its antiderivative

F

.

Questions Title:

Function

f

Answers Title:

Antiderivative

F

Question 1:

f (x) = \sqrt{x} + \sqrt[4]{x}

Answer 1:

F (x) = \frac{2 \sqrt{x^{3}}}{3} + \frac{4 \sqrt[4]{x^{5}}}{5}

Question 2:

f (x) = \frac{x + 1}{\sqrt{x}}

Answer 2:

F (x) = \frac{2 \sqrt{x^{3}}}{3} + 2 \sqrt{x}

Question 3:

f (x) = \sqrt{x} (1 + \sqrt[3]{x})

Answer 3:

F (x) = \frac{2 \sqrt{x^{3}}}{3} + \frac{6 \sqrt[6]{x^{11}}}{11}

Question 4:

f (x) = \frac{4 - x}{2 - \sqrt{x}}

Answer 4:

F (x) = \frac{2 \sqrt{x^{3}}}{3} + 2 x

Answer 5:

$F (x) = \frac{\sqrt{x^{3}}}{3} + 2 \sqrt{x}$

Answer 6:

F (x) = \frac{\sqrt{x^{3}}}{6} + 2 x