IB Mathematics Applications & Interpretation Topic SL…

A farmer is planning a new orchard. The shape of one section is defined by the region bounded by the curve $g(t) = t^2 + t$ , the $t$ -axis, and the vertical line $t = 4$ , where $t$ and $g(t)$ are measured in metres.

Divide the interval $[0, 4]$ into 4 equal sub-intervals and the $t$ -values of the endpoints.

the value of $g(t)$ at each endpoint.

Let $g(x)=-x^2+4x+2$ .

For all real $x$ , the curve $y=f(x)$ passes through the points and , and its second derivative is . an expression for .

The velocity of a particle, $v$ m s $^{-1}$ , is modelled by the function $v (t) = - 3 t^{2} + 18$ for , where is the time in seconds.

An architect is designing a glass panel. The shape of the panel is defined by the region bounded by the curve $g(x)=x^2+2x$ , the -axis, and the vertical line , where and are measured in metres.

Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the orchard section, giving your answer in $\text{m}^2$ .

the exact area of the orchard section by integrating $g(t)$ from 0 to 4, giving your answer in $\text{m}^2$ .

the approximation with the exact value and the difference.

the indefinite integral $\int g(x)\,dx$ .

the area enclosed between the graph of $y=g(x)$ and the $x$ -axis for $0\le x\le 3$ .

Find the values of $t$ for which the velocity is zero.

Find $\max_{0\leq t\leq 4}|v(t)|$ .

Assuming the particle is at the origin at $t=0$ , find an expression for the displacement $s$ (in metres) of the particle at time $t$ seconds.

the total distance travelled, including both forward and backward motion, in the interval $0\leq t\leq 3$ .

Divide the interval $[0,4]$ into 4 equal sub-intervals and the $x$ -values of the endpoints.

the value of $g(x)$ at each endpoint.

Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the panel, giving your answer in $\text{m}^2$ .

the exact area of the panel by integrating $g(x)$ from 0 to 4, giving your answer in $\text{m}^2$ .

the approximation with the exact value and the difference.

IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 5.5—introduction to Integration Questionbank