Mathematics Integration Level: Misc Level
Special type
Rule to evaluate
or
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
Mathematics Integration Level: Misc Level
Special type
Rule to evaluate
or
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
Mathematics Integration Level: Misc Level
Special type
Rule to evaluate
or
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
Physics Wave Optics Level: Misc Level
Consider two diffraction gratings with the same slit separation, the only difference being that one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic,
a. both gratings produce the same separation between orders.
b. both gratings produce the same separation between orders, but the orders are better defined with the 4- slit grating.
c. the grating with 3 slits produces the greater separation between orders.
d. the grating with 4 slits produces the greater separation between orders.
Mathematics Integration Level: Misc Level
Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute to make partial fractions. Once the partial fractions are formed substitute back
and integrate.
Mathematics Integration Level: Misc Level
Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute to make partial fractions. Once the partial fractions are formed substitute back
and integrate.
Mathematics Integration Level: Misc Level
Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute to make partial fractions. Once the partial fractions are formed substitute back
and integrate.
Mathematics Integration Level: Misc Level
Special type (Partial fraction)
When only even powers of x occur in the numerator as well as the denominator, substitute to make partial fractions. Once the partial fractions are formed substitute back
and integrate.
Mathematics Integration Level: Misc Level
Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential
Mathematics Integration Level: Misc Level
Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential
Mathematics Integration Level: Misc Level
Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential
Mathematics Integration Level: Misc Level
Integerate the following by parts by using ILATE.
I = inverse trigonometric
L = logarithmic
A = algebraic
T = trigonometric
E = exponential
Physics Properties Of Matter Level: Misc Level
The weight that will cause a wire of diameter d to stretch a given distance, for a fixed length of wire, is
a. proportional to d.
b. proportional to d 2.
c. independent of what the length of the wire is.
d. independent of d.
Physics Properties Of Matter Level: Misc Level
A copper wire is found to break when subjected to minimum tension of 36 N. If the wire diameter were half as great, we would expect the wire to break when subjected to a minimum tension of ?
Physics Wave Optics Level: Misc Level
The index of refraction of diamond is 2.42. This means that a given wavelength of light travel
a. 2.42 times faster in diamond than it does in vacuum.
b. 2.42 times faster in vacuum than it does in diamond.
c. 2.42 times faster in diamond than it does in air.
d. 2.42 times faster in air than it does in diamond.
