Find a curve from its gradient and a point

Question 1

A cyclist's velocity is v = 2 + 2t m/s. Starting from s = 0, how far has she travelled after 5 seconds?

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Question 2

dy/dx = −8x − 5 and the curve passes through (0, 7). Find y in terms of x.

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Question 3

A cyclist's velocity is v = 1 + 4t m/s. Starting from s = 0, how far has she travelled after 2 seconds?

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Question 4

dy/dx = −8x − 2 and the curve passes through (−1, 2). Find y in terms of x.

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Question 5

A cyclist's velocity is v = 2 + 6t m/s. Starting from s = 0, how far has she travelled after 6 seconds?

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Question 6

dy/dx = 4x + 3 and the curve passes through (3, 5). Find y in terms of x.

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Question 7

A cyclist's velocity is v = 2 + 4t m/s. Starting from s = 0, how far has she travelled after 6 seconds?

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Question 8

dy/dx = 4x − 3 and the curve passes through (−2, 2). Find y in terms of x.

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Question 9

A cyclist's velocity is v = 2 + 2t m/s. Starting from s = 0, how far has she travelled after 6 seconds?

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Question 10

dy/dx = −8x + 5 and the curve passes through (1, 0). Find y in terms of x.

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Question 11

A cyclist's velocity is v = 4 + 8t m/s. Starting from s = 0, how far has she travelled after 6 seconds?

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Question 12

dy/dx = −8x + 4 and the curve passes through (2, −3). Find y in terms of x.

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Question 13

A cyclist's velocity is v = 3 + 2t m/s. Starting from s = 0, how far has she travelled after 5 seconds?

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Question 14

dy/dx = −6x and the curve passes through (−1, 5). Find y in terms of x.

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Question 15

A cyclist's velocity is v = 4 + 8t m/s. Starting from s = 0, how far has she travelled after 6 seconds?

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Question 16

dy/dx = −4x − 2 and the curve passes through (1, 7). Find y in terms of x.

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