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Exercises for Question Type 2: Integrating polynomials with boundary conditions to solve for C - IB | RevisionDojo

Question 1

The question asks for the antiderivative of a polynomial function given an initial condition, which involves integration and solving for the constant of integration.

Find the function $y(x)$ if $y' = -5x^3 + x - 1$ and $y(1)=-2$ .

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Question 2

If $y' = 4x^4 - x^3 + 6x$ and $y(-1)=0$ , determine an expression for $y(x)$ .

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Question 3

Given $y' = 8x^4 + 2x^3 + 11x + 3$ and the initial condition $y(1)=9$ , find $y(x)$ .

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Question 4

Find $y(x)$ given $y' = 7x^2 - 3x + 2$ and the condition $y(3)=50$ .

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Question 5

Determine $y(x)$ if $y' = 2x^3 + 5x^2 - x + 4$ and $y(1)=3$ .

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Question 6

Given that $y' = 2x^6 - x^4 + 4x^2 - 2$ and $y(-2) = 5$ , find an expression for $y$ in terms of $x$ .

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Question 7

Given $y' = 5x^2 + 3$ and $y(0) = 1$ , find $y(x)$ .

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Question 8

Find $y(x)$ if $y' = 6x^5 + x^2 - 3$ and $y(1)=10$ .

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Question 9

If $y' = 5x^3 - 4x^2 + 7x - 2$ and $y(0)=5$ , determine $y(x)$ .

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Question 10

The question asks for the antiderivative of a polynomial function given an initial condition to determine the constant of integration.

Given $y' = 3x^2 + 2x + 1$ with $y(2)=20$ , find the function $y(x)$ .

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Question 11

Given that $y' = x^5 - 2x^3 + x$ and $y(2) = 15$ , determine an expression for $y$ in terms of $x$ .

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Question 12

Determine $y(x)$ if $y' = 9x^4 + 8x$ and $y(0)=7$ .

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Question Type 2: Integrating polynomials with boundary conditions to solve for C Exercises