# A-AS Level (CIE) Mathematics Paper-1: Specimen Questions with Answers 12 - 13 of 20

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## Question 12

## Question 13

### Question

MCQ▾The value of the integral is________

### Choices

Choice (4) | |
---|---|

a. | |

b. | |

c. | |

d. |

### Answer

c.### Explanation

**Definite Integral as Limit of Sum**:

The definite integral of any function can be expressed either as the limit of a sum or if there exists an antiderivative for the interval , then the definite integral of the function is the difference of the values at points and . Let us discuss definite integrals as a limit of a sum. Consider a continuous function in defined in the closed interval . Assuming that , the following graph depicts in .

The integral of is the area of the region bounded by the curve . This area is represented by the region as shown in the above figure. This entire region lying between is divided into n equal subintervals given by .

Let us consider the width of each subinterval as such that and . Also, in the above representation.

From the first inequality, considering any arbitrary subinterval where , it can be said that, area of the region

Since, , the rectangular strips are very narrow, it can be assumed that the limiting values of and are equal and the common limiting value gives us the area under the curve, i.e.. ,