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Differentiation by Substitution
Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily. If f(x) involves inverse trigonometric functions of..
Differentiation by Substitution
Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily.Differentiation of certain functions seem to be very d..
Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily.Differentiation of certain functions seem to be very d..Integration by Substitution
Integration of the form - Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..
Integration of the form - Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..Formation of a Differential Equation
Consider the family of lines represented by y = mx .(1)Consider the family of lines represented by y = mx .(1) This equation represents infinite number of lines passing through the origin. Differentiating (1), we get Substituting this value of m, we get the differential..
Consider the family of lines represented by y = mx .(1)Consider the family of lines represented by y = mx .(1) This equation represents infinite number of lines passing through the origin. Differentiating (1), we get Substituting this value of m, we get the differential..Working rule for Evaluating Definite Integral with Suitable Substitution
Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Writ..
Suppose we have to evaluate the integral (1) Let t = g(x) is the suitable substitution. Differentiating, we get dt = g'(x) dx (2) Now the new variable is t. The upper limit b and the lower limit a are in terms of x. Change these limits to the new variable g(b) and g(a). (3) Writ..Step II:
Substituting in the differential equation ..
Substituting in the differential equation ..Suggested answer:
y 2 = 4ax (1) Differentiating with respect to x Substitute for 4a in (1), we get y - 2xy' = 0 Note that the given equation is differentiated only once to obtain the differential equation since it has only one consta..
y 2 = 4ax (1) Differentiating with respect to x Substitute for 4a in (1), we get y - 2xy' = 0 Note that the given equation is differentiated only once to obtain the differential equation since it has only one consta..Integrated Rate Equation For First Order Reaction
For the reaction A Products, which follows first order kinetics, the rate of the reaction is proportional to the concentration of A raised to power 1. i.e., Integration of the differential equation gives In [A] = - kt + constant At t = 0, [A] = [A] o ln [A] o = constant On ..
For the reaction A Products, which follows first order kinetics, the rate of the reaction is proportional to the concentration of A raised to power 1. i.e., Integration of the differential equation gives In [A] = - kt + constant At t = 0, [A] = [A] o ln [A] o = constant On ..Rate of Disintegration
where l is a constant of proportionality which is called by Rutherford and Soddy as Radioactive (or decay or disintegration) constant. The rate of disintegration has a negative sign showing that the number of atoms of A decreases with time. In the differential form, the equation is Integr..
where l is a constant of proportionality which is called by Rutherford and Soddy as Radioactive (or decay or disintegration) constant. The rate of disintegration has a negative sign showing that the number of atoms of A decreases with time. In the differential form, the equation is Integr..See what our Users say :
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