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5196

Physics Wave Optics Level: Misc Level

The index of refraction of diamond is 2.42. This means that a given wavelength of light travels

2.42 times faster in vacuum than it does in diamond.

2.42 times faster in air than it does in diamond.

2.42 times faster in diamond than it does in vacuum.

2.42 times faster in diamond than it does in air.

5195

Physics Current Electricity Level: Misc Level

a time delay of 25 ms is required for the voltage to fall to 20% of its maximum value.rearrange the equation to find a new value of resistance to achieve this if the capacitance is kept the same.

5189

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int [Sin(logx)+Cos(log(x))]dx$

5188

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int (Cosx+3Sinx)e^{3x}dx$

5187

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{2+Sin2x}{1+Cos2x}e^{x}dx$

5186

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{xe^{2x}}{(1+2x)^{2}}dx$

5185

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{x-1}{(x+1)^{3}}e^{x}dx$

5184

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(Cotx+log|Sinx|)dx$

5183

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{2x-1}{4x^{2}}e^{2x}dx$

5182

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

If $\int \frac{x-1}{x^{2}}e^{x}dx=f(x)e^{x}+c$ then find f(x)

5181

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int (x+1)e^{x}dx$

5180

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(Cotx+Cosec^{2}x)dx$

5179

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(tanx+Sec^{2}x)dx$

5178

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \sqrt{Cotx}dx$

5177

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \frac{x^{2}-3x+1}{x^{4}-x^{2}+1}dx$

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