4 int_0^1 left(frac{1}{sqrt{3+x^2}+sqrt{1+x^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) ધારો કે $I = 4 \int_0^1 \frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}} dx - 3 \ln \sqrt{3}$.સંકલિતનું સંમેયીકરણ કરતા:$I = 4 \int_0^1 \frac{\sqrt{3+x^2}-\sqrt

Vedclass · Accepted Answer

$2-\sqrt{2}-\log_e(1+\sqrt{2})$

Vedclass · Answer

(B) ધારો કે $I = 4 \int_0^1 \frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}} dx - 3 \ln \sqrt{3}$.સંકલિતનું સંમેયીકરણ કરતા:$I = 4 \int_0^1 \frac{\sqrt{3+x^2}-\sqrt{1+x^2}}{(3+x^2)-(1+x^2)} dx - \frac{3}{2} \ln 3$$I = 4 \int_0^1 \frac{\sqrt{3+x^2}-\sqrt{1+x^2}}{2} dx - \frac{3}{2} \ln 3$$I = 2 \int_0^1 \sqrt{3+x^2} dx - 2 \int_0^1 \sqrt{1+x^2} dx - \frac{3}{2} \ln 3$સૂત્ર $\int \sqrt{a^2+x^2} dx = \frac{x}{2}\sqrt{a^2+x^2} + \frac{a^2}{2}\ln(x+\sqrt{a^2+x^2})$ નો ઉપયોગ કરતા:$I = 2 \left[ \frac{x}{2}\sqrt{3+x^2} + \frac{3}{2}\ln(x+\sqrt{3+x^2}) \right]_0^1 - 2 \left[ \frac{x}{2}\sqrt{1+x^2} + \frac{1}{2}\ln(x+\sqrt{1+x^2}) \right]_0^1 - \frac{3}{2} \ln 3$$I = \left[ x\sqrt{3+x^2} + 3\ln(x+\sqrt{3+x^2}) \right]_0^1 - \left[ x\sqrt{1+x^2} + \ln(x+\sqrt{1+x^2}) \right]_0^1 - \frac{3}{2} \ln 3$$I = (1\sqrt{4} + 3\ln(1+2) - (0 + 3\ln\sqrt{3})) - (1\sqrt{2} + \ln(1+\sqrt{2}) - (0 + \ln 1)) - \frac{3}{2} \ln 3$$I = (2 + 3\ln 3 - \frac{3}{2}\ln 3) - (\sqrt{2} + \ln(1+\sqrt{2})) - \frac{3}{2} \ln 3$$I = 2 + \frac{3}{2}\ln 3 - \sqrt{2} - \ln(1+\sqrt{2}) - \frac{3}{2} \ln 3$$I = 2 - \sqrt{2} - \ln(1+\sqrt{2})$.

$4 \int_0^1 \left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) dx - 3 \log_e(\sqrt{3})$ ની કિંમત શોધો :

Similar Questions

જો $f(x) = |x| + |x - 1| + |x - 2|$,$x \in R$ હોય,તો $\int_{0}^{3} f(x) \, dx = $

$\int_{-1}^1 \frac{|x|}{x} \, dx$ ની કિંમત શોધો.

સંકલન $\int_{1}^{5}[|x-3|+|1-x|] dx$ નું મૂલ્ય કેટલું થાય?

$\int_{\pi / 6}^{\pi / 3} \cos^{-4} x \, dx =$

ધારો કે $I = \int_{0}^{1} \frac{\sin x}{\sqrt{x}} \, dx$ અને $J = \int_{0}^{1} \frac{\cos x}{\sqrt{x}} \, dx$. તો નીચેનામાંથી કયું સાચું છે?

Vedclass Test Series

Exam Paper Generator

Online Exam Module