STDs

Gujarat Board Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Ex 6.5 Question 1. Find the maximum and minimum values, if any, of the following functions given by (i) f(x) = (2x – 1)² + 3 (ii) f(x) = 9x² + 12x + 2 (iii) f(x) = – (x -1)² + 10 (iv) […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.1 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.1 Find an antiderivative (or integral) of the following by the method of inspection: Question 1. sin 2x Solution: We know that (frac{d}{dx}) cos 2x = – 2sin 2x. or (frac{d}{dx}) (- […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.2 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.2 Integrate the following: Question 1. (frac{2 x}{1+x^{2}}) Solution: Question 2. (frac{(log x)^{2}}{x}) Solution: Question 3. (frac{1}{x+xlogx}) Solution: I = ∫(frac{1}{t})dt = log t + C = log |1 + log x| […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.3 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.3 Find the integrals of the following: Question 1. sin2(2x + 5) Solution: Question 2. sin3x cos4x Solution: Question 3. cos2x cos4x cos6x Solution: Question 4. sin3(2x + 1) Solution: Question 5. […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4 Integrate the following functions: Question 1. (frac{3 x^{2}}{x^{6}+1}) Solution: Question 2. (frac{1}{sqrt{1+4 x^{2}}}) Solution: Question 3. (frac{dx}{sqrt{(2-x)^{2}+1}}) Solution: Question 4. (frac{dx}{sqrt{9-25 x^{2}}}) Solution: Question 5. (frac{3 x}{1+2 x^{4}}) Solution: Question 6. […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.5 Integrate the following functions: Question 1. (frac{x}{(x+1)(x+2)}) Solution: (frac{x}{(x+1)(x+2)}) may be written as (frac{x}{(x+1)(x+2)}) = (frac{A}{x+1}) + (frac{B}{x+2}) ∴ x = A(x + 2) + B(x + 1) Put x = – 1, – 1 = A(- 1 + 2) + 0 = […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.6 Integrate the following functions: Question 1. x sin x Solution: Let I = ∫x sin x dx We know that ∫uv dx = u∫v dx – ∫(u’ ∫v dx)dx Put u = x and v = sin x. ∴ I = x ∫sin […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.7 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.7 Integrate the following functions: Question 1. (sqrt{4-x^{2}}) Solution: Question 2. (sqrt{1-4x^{2}}) Solution: Question 3. (sqrt{x^{2}+4 x+6}) Solution: Question 4. (sqrt{x^{2}+4 x+1}) Solution: Question 5. (sqrt{1-4 x-x^{2}}) Solution: Question 6. (sqrt{x^{2}+4 x-5}) […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.8 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.8 Evaluate the following definite integrals as limits of the sum: Question 1. (int_{a}^{b}) x dx Solution: Question 2. (int_{5}^{0}) (x + 1) dx Solution: Compare (int_{5}^{0}) (x + 1) dx with […]