# Worksheet: Antiderivatives of Functions

In this worksheet, we will practice finding the antiderivative of a given function.

**Q1: **

Determine the most general antiderivative of the function .

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**Q3: **

If , determine .

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**Q4: **

Find the most general antiderivative of the function .

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**Q5: **

Determine the most general antiderivative of the function .

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**Q6: **

Determine the antiderivative of the function where .

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**Q7: **

Determine the most general antiderivative of the function , given that .

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**Q8: **

Determine the most general antiderivative of the function .

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**Q9: **

Find the most general antiderivative of the function .

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**Q10: **

Find the most general antiderivative of the function .

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**Q11: **

Find the most general antiderivative of the function .

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**Q12: **

Determine the most general antiderivative of the function .

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**Q13: **

Determine the most general antiderivative of the function .

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**Q14: **

Find the most general antiderivative of the function .

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**Q15: **

Find, if possible, an antiderivative of that satisfies the conditions and .

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- BNo such antiderivative exists.

**Q16: **

What is the antiderivative of that satisfies ?

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**Q17: **

Determine the most general antiderivative of the function if and .

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**Q18: **

By considering the product rule, find a function so that .

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**Q19: **

Find the most general antiderivative of the function .

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**Q20: **

Determine the most general antiderivative of the function .

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**Q21: **

Determine the family of functions for which .

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**Q22: **

If the rate of change in the area of a metallic plate with respect to time due to heating is given by the relation where the area is in square metres, and the time is in minutes, given that when , find, correct to the nearest two decimal places, the area of the plate just before heating.

**Q23: **

The second derivative of a function is and the equation of the tangent to its graph at is . Find the equation of the curve.

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**Q24: **

Suppose that and when . Find in terms of .

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**Q25: **

Find the function of the curve whose first derivative is and the function equals 7 when equals .

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