ISC Class 12 Integrals and Applications — practice questions — page 4

Explore 97 free Integrals and Applications questions in ISC Class 12 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integrals and Applications questions and exercises with answers

Showing questions 91–97 of 97.

For the region below the axis A1 is negative while A2 is:Read the answer and worked solution →The number of arbitrary constants in the general solution of a differential equation of order $n$ is:Read the answer and worked solution →True or false: calculusRead the answer and worked solution →True or false about areasRead the answer and worked solution →The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2$ is:Read the answer and worked solution →Finding the area of a circle here uses which curves in standard form?Read the answer and worked solution →Formulae of elementary geometry cannot find areas enclosed by:Read the answer and worked solution →

Worked practice questions

For the region below the axis A1 is negative while A2 is:

Zero only
Doubled
Positive
Negative

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Correct answer: C. Positive

1. A1 comes from the part beneath the axis. 2. A2 comes from the part above it. 3. So A2 is positive. 4. The answer is positive. _Source: syllabus Mathematics, Ch 8 'Application of Integrals'_

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The number of arbitrary constants in the general solution of a differential equation of order $n$ is:

$n$
$0$
$1$
$n - 1$

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Correct answer: A. $n$

By definition, the general solution of an $n$-th order differential equation contains exactly $n$ independent arbitrary constants, matching the order of the equation. For example, $\dfrac{d^2y}{dx^2} + y = 0$ has the general solution $y = A\cos x + B\sin x$ with two constants $A$ and $B$, since the equation is of order 2.

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True or false: calculus

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Questions

Statement is true
Yes
Statement
Integration is the inverse process of differentiation.
Statement is true
Yes
Statement
An indefinite integral needs a constant of integration.
Statement is true
Yes
Statement
A derivative can give the equation of a tangent to a curve.
Statement is true
No
Statement
A definite integral always leaves an arbitrary constant behind.

Instructions

Decide whether each statement about calculus is true or false.

_Source: syllabus Maths Ch7 Integrals, INTEGRALS_

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