Let f (x) , x ≥ 0 , be a non negative continuous function and let $ F (x) = \int_{0}^{x}f(t)dt $ , x ≥ 0 . If for some c > 0, f (x) ≤ c ….
Q: Let f (x) , x ≥ 0 , be a non negative continuous function and let $ F (x)…
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Q: Let f (x) , x ≥ 0 , be a non negative continuous function and let $ F (x)…
Q: Function f (x) is defined as $\displaystyle f(x) = x^2 + \int_{-1}^{1} (x^2 + t^2 x^3 )(f (t) –…
Q: Evaluate $\displaystyle \int_{0}^{t} [|sin^{-1}(sinx)|]dx $ Where t ∈ ( 2nπ , (8n+1)π/4 ) Solution : Since the function is…
Q: $\displaystyle \int_{-1/\sqrt{3}}^{1/\sqrt{3}} \frac{cos^{-1}\frac{2x}{1+x^2} + tan^{-1}\frac{2x}{1-x^2}}{e^x +1}$ Solution : Let tan-1x = θ $\displaystyle – 1/\sqrt{3} \le x \le 1/\sqrt{3}$…
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Q: Show that the value of $\frac{tanx}{tan3x} $ , whenever defined, never lies between 1/3 and 3. Solution : Let…