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.
    Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]


      • 2.
        For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

          • local maximum value is 2
          • local minimum value is \( -2 \)
          • local maximum value is \( -2 \)
          • local minimum value \( < \) local maximum value

        • 3.
          Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]


            • 4.
              Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
              Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

                • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
                • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
                • Assertion (A) is true and Reason (R) is false.
                • Assertion (A) is false and Reason (R) is true.

              • 5.
                If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]


                  • 6.

                    For two vectors \(\vec{a}\) and \(\vec{b}\):  

                    Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

                      • Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
                      • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
                      • Assertion (A) is true, but Reason (R) is false.
                      • Assertion (A) is false, but Reason (R) is true.
                    CBSE CLASS XII Previous Year Papers

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