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SingaporeAdditional Mathematics

Integration and Its Applications

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we find the area of a region enclosed between two curves, or between a curve and a line?

Find the area enclosed between two curves, or a curve and a line, by integrating the difference of the upper and lower functions between their intersection points
A focused answer to the O-Level A-Maths outcome on area between curves. Finding intersection points as limits and integrating the upper minus the lower function to get the enclosed area.
9 min answer →

How does a definite integral give the area under a curve, and how do we evaluate it?

Evaluate definite integrals using limits and use them to find the area of a region bounded by a curve and the x-axis
A focused answer to the O-Level A-Maths outcome on definite integrals. Evaluating an integral between limits, the meaning as area under a curve, and handling regions below the x-axis.
9 min answer →

How is integration the reverse of differentiation, and how do we integrate powers and standard functions?

Integrate powers of x and standard functions as the reverse of differentiation, including the constant of integration, and integrate linear composites
A focused answer to the O-Level A-Maths outcome on indefinite integration. Reversing the power rule, the constant of integration, the standard integrals, and integrating functions of a linear expression.
9 min answer →

How do we integrate exponential, reciprocal and trigonometric functions, including those of a linear expression?

Integrate the exponential, reciprocal and trigonometric functions and their linear composites as the reverse of the corresponding derivatives
A focused answer to the O-Level A-Maths outcome on integrating standard functions. The integrals of the exponential, reciprocal and trigonometric functions, and the rule for a linear composite.
9 min answer →