Integration Problems

1 Using the infinite primitive functions of y = x² − x + 1, for what values of the function does x = 3 take the value of 5?

2Write the primitive function of y = x² + 2x whose graph passes through the point (1, 3).

3 Find the function F(x) whose derivative is f(x) = x + 6 and for x = 2 takes the value of 25.

4Find a line whose slope is 2 and passes through the point P (0, 4).

5Calculate the equation of the curve through P (1, 5) and whose slope at any point is 3x² + 5x − 2.

6Find the antiderivative of the function función, which is annuled for x = 2.


1

Using the infinite primitive functions of y = x² − x + 1, for what values of the function does x = 3 take the value of 5?

Integral Operations

Integral Operations

x = 3 y = 5

Integral Operations

Integral Constant

Integration Solution


2

Write the primitive function of y = x² + 2x whose graph passes through the point (1, 3).

Integral Operations

Integral Operations

Integral Constant

Integration Solution


3

Find the function F(x) whose derivative is f(x) = x + 6 and for x = 2 takes the value of 25.

Integral Operations

Integral Constant

Integration Solution


4

Find a line whose slope is 2 and passes through the point P (0, 4).

f '(x) = 2

f(x) = 2x + C

4 = 2 · 0 + C

f(x) = 2x + 4


5

Calculate the equation of the curve through P (1, 5) and whose slope at any point is 3x² + 5x − 2.

Integral Operations

Integral Operations

Integral Constant

Integration Solution


6

Find the antiderivative of the function función, which is annuled for x = 2.

Integral Operations

Integral Constant

Integration Solution




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