Finding Areas by Integration (HSC SSCE Mathematics Advanced): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is the key difference between an area and a definite integral?
What is the key difference between an area and a definite integral?
An area is always positive; an integral can be negative
What is the first step in the three-step method for finding areas by integration?
What is the first step in the three-step method for finding areas by integration?
Draw a sketch showing intercepts and intersections
When a curve sits completely above the -axis, what is true about the definite integral?
When a curve sits completely above the -axis, what is true about the definite integral?
It is positive and equals the area
How do you find the area when a curve lies completely below the -axis?
How do you find the area when a curve lies completely below the -axis?
Take the absolute value of the integral
What must you do when a curve crosses the -axis to find the total area?
What must you do when a curve crosses the -axis to find the total area?
Split at x-intercepts and add absolute values
What is the defining property of an odd function ?
What is the defining property of an odd function ?
for all in its domain
What type of symmetry do odd functions have graphically?
What type of symmetry do odd functions have graphically?
Rotational symmetry of 180° about the origin
How can symmetry of odd functions simplify area calculations?
How can symmetry of odd functions simplify area calculations?
Calculate one region's area and double it
In integration with respect to , what are the limits of integration?
In integration with respect to , what are the limits of integration?
-values rather than -values
When is it useful to integrate with respect to instead of ?
When is it useful to integrate with respect to instead of ?
When the region is easier to describe using