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# Integrals

At Saralstudy, we are providing you with the solution of Class 12th mathematics Integrals according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Integrals so that you can prepare for the exam according to your own pace and your speed.

Integration is an inverse process of differentiation. In this chapter, we will learn how to find the integral of a function. Its knowledge in calculus is very much needed for finding the areas under curves, etc. This chapter consists of integration of a variety of functions by substitutions, by parts and by partial fractions. Definite integrals as a limit of a sum , fundamental theorem of calculus, properties of definite integrals.

Download pdf of NCERT Examplar with Solutions for Class mathematics Chapter 7 Integrals ### Exercise 1

•  Q1 Integrals sin 2x Q2 Integrals cos3x Q3 Integrals e2x Q4 Integrals (ax + b)2 Q5 sin 2x – 4e3x Q6 \begin{align} \int \left(4e^{3x} + 1\right).dx \end{align} Q7 \begin{align} \int x^2\left(1 - \frac{1}{x^2}\right).dx \end{align} Q8 \begin{align} \int \left({a}{x^2} + bx + c\right) .dx\end{align} Q9 \begin{align} \int \left({2}{x^2} + e^x\right) .dx\end{align} Q10 \begin{align} \int \left(\sqrt{x} - \frac {1}{\sqrt{x}}\right)^2 .dx\end{align} Q11 \begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align} Q12 \begin{align} \int \frac{x^3 + 3x + 4}{\sqrt{x}} . dx\end{align} Q13 \begin{align} \int \frac{x^3 - x^2 + x - 1}{x-1} . dx\end{align} Q14 \begin{align} \int\left(1-x\right).\sqrt {x}.dx\end{align} Q15 \begin{align} \int\sqrt {x}.\left(3x^2+2x + 3\right).dx\end{align} Q16 \begin{align} \int\left(2x - 3Cosx + e^x\right).dx\end{align} Q17 \begin{align} \int\left(2x^2-3Sinx +5\sqrt {x}\right).dx\end{align} Q18 \begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align} Q19 \begin{align} \int \frac {sec^2 x}{Coses^2 x} . dx\end{align} Q20 \begin{align} \int \left(\frac {2-3sin x}{cos^2 x}\right) . dx\end{align} Q21 The anti derivative of \begin{align} \left(\sqrt x + \frac {1}{\sqrt x}\right)\end{align} equals to \begin{align} (A) \frac{1}{3}.x^\frac{1}{3} + 2.x^\frac{1}{2} +C \;\;\;\; (B) \frac{2}{3}.x^\frac{2}{3} + \frac{1}{2}.x^2 +C \end{align} \begin{align} (C) \frac{2}{3}.x^\frac{3}{2} +2 x^\frac{1}{2} +C \;\;\;\;(D) \frac{3}{2}.x^\frac{3}{2} +\frac{1}{2}. x^\frac{1}{2} +C \end{align} Q22 If \begin{align} \frac{d}{dx} f(x) = 4x^3 - \frac{3}{x^4}\end{align} such that f(2) = 0 , then f(x) is \begin{align} (A) x^4 + \frac {1}{x^3} - \frac{129}{8} \;\;\;\;(B) x^3 + \frac{1}{x^4} + \frac{129}{8}\end{align}\begin{align} (c) x^3 + \frac {1}{x^4} + \frac{129}{8} \;\;\;\;(D) x^3 + \frac{1}{x^4} - \frac{129}{8}\end{align}

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