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Indefinite integrals are also called general integrals. C is called constant of integration. All these integrals differ by a constant. From the geometric point of view, an indefinite integral is...
A change in the variable of integration often reduces an integral to one of the fundamental integrals. The method in which you change the variable to some other variable is called the method of...
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sin2A = 2sinA cosA cos2A = 2cos²A - 1 = 1 - 2sin²A ∫ sinx dx = -cosx + C ∫ cosx dx = sinx + C ∫ sin⁴x cos⁶x dx = ∫ sin⁴x cos⁴x cos²x dx = (1/16) ∫ 16 sin⁴x cos⁴x...
The given equation is: Let’s assume a general solution as: Therefore, we get: Therefore the general solution is:
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Let: u = sin(2x) du = 2cos(2x) dx dv = e^x dx v = e^x Then: L = uv - ∫ v du ==> L = e^x*sin(2x) - 2 ∫ e^x*cos(2x) dx Let: u = cos(2x) du = -2sin(2x) dv = e^x dx v = e^x By another round of integration...
yhe answer for 1/cosx.dx wil be ln {tan mod (pie/4 + x/2) mod}+c
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look in this question se can write sin^2x as 1-cos^2x so substitute this value in the above expression and then try to make something in terms of cos2x afterall open the square and do the need full
you will have to expand it as if cosx = 1-tan^2(x)/1+tan^2(x) yet now you can make is telescopic series type function and integrate diffrently
let me help u by taking an example as sinx.cosx.dx u know that d(cosx) = sinx.dx so now we can interpret as cosx.dcosx thus we will get cos^2(x)/2
invariance is a methodolgy used in case of integration it is a faster way to solve the questions in an easy manner
anti derivative means integration and its value equals theta1 theta2 ∫sinx.dx = -cos(theta1-theta2) +c approve if useful
in which function comprising limit we have to integrate?
its done final answer will be in terms of Q(theta) put (phi) 1/2 = sint for 1 integral and cost for second integral when u replace d phi by dt it forms t sin2t for first one so on putting the limits...
answer is 2pi using king property we get the integral as (cospx+sinqx) 2 now add both of integrals and we get 2I=2(cos 2 px+sin 2 qx) and change the limits to 0 – pi use property that 1+cos2x=2cos 2 x...
dx/sinx^6+(1-sinx^2)^3 dx/sinx^6+1-sinx^6-3sinx^2+3sinx^4 dx/3sinx^4-3sinx^2+1 dx/-3sinx^2(1-sinx^2)+1 dx/-3sinx^2cosx^2+1 4dx/4-3sin2x now sin2x=2tanx/1+tanx^2 secx^2 dx/tanx^2-1.5tanx+1 put tanx=t...
Hello student, The given question is Let I = = = = I 1 - I 2 Now, considering these one by one
Hello student, The given question is Let I = = = = I 1 – I 2 Now, we have
Hello student, First of all, in order to excel in integral calculus the inetgration formulae should be on your finger tips. There is no shortcut to hardwork and practice, but yes, there are some...
Hello student, The given term is = I 101 = = = = -5050(I 101 - I 100 ) So, 5051 I 101 = 5050 I 100 So, 5050 (I 100 /I 101 ) = 5051
= 0
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