NCERT Solutions for Applications of Integrals Exercise 8.1 Solutions

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Class 12 Maths NCERT Solutions Chapter 8 Applications of Integrals Exercise 8.1 is provided in the article. Class 12 Chapter 8 Applications of Integrals Exercises include questions on area between a curve, parabola, and ellipse.

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CBSE CLASS XII Related Questions

  • 1.
    Find \( \int \frac{3x + 1}{(x - 2)^2 (x + 2)} \, dx \)


      • 2.
        Let \( \vec{a} \) be a position vector whose tip is the point (2, -3). If \( \overrightarrow{AB} = \vec{a} \), where coordinates of A are (–4, 5), then the coordinates of B are:

          • (-2, -2)
          • (2, -2)
          • (-2, 2)
          • (2, 2)

        • 3.
          $ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :

            • $x + C$
            • $\frac{x^2}{2} + C$
            • $\frac{x^4}{4} + C$
            • $\frac{x^3}{3} + C$

          • 4.

            The given graph illustrates:

              • $y = \tan^{-1} x$
              • $y = \csc^{-1} x$
              • $y = \cot^{-1} x$
              • $y = \sec^{-1} x$

            • 5.
              Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

                • $[5, 10]$
                • $[-2, 5]$
                • $[2, 1]$
                • $[-10, 5]$

              • 6.
                For a function $f(x)$, which of the following holds true?

                  • $\int_a^b f(x) dx = \int_a^b f(a + b - x) dx$
                  • $\int_a^b f(x) dx = 0$, if $f$ is an even function
                  • $\int_a^b f(x) dx = 2 \int_0^a f(x) dx$, if $f$ is an odd function
                  • $\int_0^a f(x) dx = \int_0^a f(2a + x) dx$
                CBSE CLASS XII Previous Year Papers

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