C2 INTEGRATION HELP (pls)

Posted a pic below

Where did that '3' come from? :/

Where did that '3' come from? :/

@boriapple @Logic4Life Thank you!

Where did that '3' come from? :/

Area of a trapezium = $\frac{a\times b}{2}\times h$ h is the height of the trapezium which you get from $x_2-x_1 = 4-1$

No problem. Good luck with the C2 exam on Wednesday!

it's exact area ... I've done this question you don't use trapezium rule.
You use the points to find the gradient of the line and then integrate the line and subtract the integral of the curve. Then you sub in the x values
If it was trapezium rule they'd say "estimate of area", but they say "exact area"
Good luck in C2 btw x

Thank you for the advice, I'll try to remember that in the exam

it's exact area ... I've done this question you don't use trapezium rule.
You use the points to find the gradient of the line and then integrate the line and subtract the integral of the curve. Then you sub in the x values




If it was trapezium rule they'd say "estimate of area", but they say "exact area"
Good luck in C2 btw x

No, the area under the line AB is a trapezium. This is what was being worked out in the solution.

that shape isn't a trapezium ... a trapezium is a four sided shape

The line PQ (which I accidentally said was AB above) has an area. This area between the limits of $x_P, x_Q$ gives a 4 sided shape, which happens to be a trapezium.

You need this area so that you can take away the area calculated from the finite integral of the curve giving the requested area.