Find the area bounded by the curve x^2-2x+3 between the limits x=0 and x=1 and the horizontal axis.

In order to find the area bounded by a curve and the horizontal axis, we must integrate the curve between the specified limits.

Firstly we must integrate the curve x^2-2x+3. To integrate a polynomial such as the one provided above, we must raise the power of each term and divide the term by the new power. Doing this will leave us with (x^3)/3 - x^2 + 3x + C. The new C term there as when integrating it is possible that a new constant can be found.

Now we must apply the limits to the newly integrated equation. This can be done by first substituing the values x=1 into the integrated equation and then minusing the integrated equation with substituted values of x=0: [(1^3)/3 - 1^2 + 3x(1) + C] - [(0^3)/3 - 0^2 + 3(0) + C] = [(1/3) - 1 + 3 + C] - [C] = 7/3.

It should be noted the C values are constant therefore cancel out.

We have now found that the area bounded by the horizontal axis, x=0, x=1 and the curve x^2-2x+3 is 7/3 units of area.

Diljot G. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathema...

3 months ago

Answered by Diljot, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

James T.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered: Maths, Physics+ 2 more

-Personal Statements-

“Second year Engineer. I love problem-solving and hard work! Everyone works differently and I will find the best way for you to learn and make sessions fun!”

£20 /hr

Andrew D.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About me Hi, I'm Andrew. I'm currently going into my second year studying maths at the University of Warwick. I find maths incredibly fascinating, as my passion stems from the idea thatmaths is everywhere and is fundamental to underst...”

£20 /hr

Jan K.

Degree: Mathematics and Music (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics


“About Myself I am a Mathematics student at Edinburgh University. I have a real passion for Mathematics, and I thouroughly enjoy explaining mathematical concepts to others. Having been home-educated all through school (which also gave ...”

About the author

£20 /hr

Diljot G.

Degree: Mechanical Engineering (Masters) - Imperial College London University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

How do I differentiate 3^2x?

A is a function of P . It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P . When P = 24 , A = 36 and when P = 18 , A = 9. Express A in terms of P .

Differentiate: y = 4x^3 - 5/x^2

Find the tangent of the following curve, y=xe^x, at x=1 expressing it in the form y=mx+c?

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss