Question Type 3: Calculating the area between a polynomial in the positive section and the x axis Exercises

Find the area between the curve $y=2x^2+3x+2$ and the x-axis from $x=0$ to $x=2$.

Find the area under $y=4x^2+1$ between $x=-1$ and $x=2$. [4 marks]

Determine the area under the curve $y=5x^4-2x^2+3$ from $x=0$ to $x=1$.

Determine the area between $y=2x^4 - x^3 + x^2 - x +1$ and the x-axis from $x=-1$ to $x=2$.

Calculate the area under the curve $y=x^2-4x+5$ above the x-axis between $x=1$ and $x=3$.

Calculate the area between the curve $y=x^3+2x^2+3x+4$ and the x-axis from $x=-1$ to $x=1$.

Find the area between $y=2x^3-3x^2+6$ and the x-axis from $x=1$ to $x=3$.

Calculate the area under $y=3x^3 - x + 2$ above the x-axis from $x=0$ to $x=2$.

Find the area between the curve $y=-x^2+4x+5$ and the x-axis for $0\le x\le2$.

Calculate the area under $y=x^5+x^4+x^3+x^2+x+1$ from $x=0$ to $x=2$.

Determine the area between $y=3x^3+x^2+2$ and the x-axis from $x=0$ to $x=2$.