STDs

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 […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.9 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.9 Evaluate the following definite integrals: Question 1. (int_{-1}^{1}) (x + 1)dx Solution: Question 2. (int_{2}^{3}) (frac{1}{x}) dx Solution: = log 3 – log 2 = log (frac{3}{2}). Question 3. (int_{1}^{2}) (4x3 […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.10 Evaluate the following integrals: Question 1. (int_{0}^{1}) (frac{x}{x^{2}+1}) dx Solution: Let I = (int_{0}^{1}) (frac{x}{x^{2}+1}) dx. Put x2 + 1 = t, 2x dx = dt. When x = 1, t = 2 and when x = 0, t = 1. ∴ I […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.11 Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.11 By using properties of definite integrals, evaluate the following: Question 1. (int_{0}^{frac{pi}{2}}) cos2x Solution: Question 2. (frac{sqrt{sin x}}{sqrt{sin x}+sqrt{cos x}})dx Solution: Question 3. (int_{0}^{frac{pi}{2}} frac{sin ^{frac{3}{2}} x}{sin ^{frac{3}{2}} x+cos ^{frac{3}{2}} x})dx […]

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Miscellaneous Exercise Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Miscellaneous Exercise Integrate the following functions w.r.t x (questions from 1 to 24): Question 1. (frac{1}{x-x^{3}}) Solution: Let (frac{1}{x-x^{3}}) = (frac{1}{x(1+x)(1-x)}) = (frac{A}{x}) + (frac{B}{1+x}) + (frac{C}{1-x}) ⇒ 1 = A(1 + x)(1 […]

Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1 Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1 Question 1. Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis. […]

Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 Question 1. Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y. Solution: Area is bounded by […]