i need some help on some integration qns here. i think it may appear to be very basic to some, but im really weak at this topic..
find the following integrals:
1. integrate (1/(sq root(1-3x)^3/2))dx
2.integrate ((2x-5)(x+2)) / sqroot x
3.integrate (e^(2x) - 4e^(-x)) square dx
4.integrate (5^(x) - 3^(2x))dx
evaluate the following definite integrals, giving your answers in exact form:
1. integrate (top:1 bottom:k) (1+(2/x))square dx, k>0.
2. integrate( top:1 bottom:0) ((2/(3x+1))+4^x) dx (my ans is 4/3 ln2 +2, dunno whether correct or not)
Hi,
First, the following are results that you need to remember:
1. integral of (ax + b)^n (n is not -1) = {(ax + b)^(n + 1)} / {a(n + 1)} + c
This will be helpful for Q1 & Q2. In Q2, you will need to expand the numerator before dividing it by sqrt(x).
2. integral of e^(ax + b) = {e^(ax + b)} / a + c
This will be applied in Q3. Again, expansion will be necessary before you integrate.
3. integral of a^(kx) = {a^(kx)} / {k(ln a)} + c
This will be used in Q4.
4. integral of 1/(ax + b) = (1/a) ln |ax + b| + c
This will be relevant to definite integral Q1, together with the use of result 1. Expansion is to be carried out first.
Definite integral Q2 needs results 4 and 3. You may use GC to verify your answer.
Thanks.
Cheers,
Wen Shih
thanks! but for qn1 and 2, what i dont know is how to do is the sqrootx part.. how to integrate sth by sq root x? for qn1, theres still the (3/2)(the qn phrase it as ³√) , which makes me very confused.
integrate ((2x-5)(x+2)) / sqroot x dx
Step 1: Expand (2x+5)(x+2)
Step 2: Divide each individual term by x^0.5. You will get 3 terms
Step 3: Integrate term by term
As for integrating a^x, I have never recommended students to memorize the integration. Simply convert it to Ln and then integrate.
Hi,
Recall the rules of indices (from O-level) in eagle's step 2 :)
Cheers,
Wen Shih
thanks! for definite integral qn 1, i got -3-k-4lnk+4/k. checked with the gc and i think im correct. is there any way of simplifying the ans?
Hi,
Simplification typically involves factorisation. Is this possible with the answer you have obtained?
Cheers,
Wen Shih
ok. i managed to do all the qns above alr. many thanks(:
pls help me with 3 more qns:
find the following integral(integral of the form f'(x) / f(x):
1. integrate cot5x / (1+cosec² 5x) dx
find the following integrals:
1. integrate ((1/cos² x)+2(sin² (4x-(π/3))))dx
2.integrate -1/2sec((π/6) - x)tan(x-(π/6))dx
Originally posted by summer2:ok. i managed to do all the qns above alr. many thanks(:
pls help me with 3 more qns:
find the following integral(integral of the form f'(x) / f(x):
1. integrate cot5x / (1+cosec² 5x) dx
find the following integrals:
1. integrate ((1/cos² x)+2(sin² (4x-(π/3))))dx
2.integrate -1/2sec((π/6) - x)tan(x-(π/6))dx
http://sg.answers.yahoo.com/dir/index;_ylt=AnJ70n_vT2g2BL7pxaNMT7oELH1G;_ylv=3?sid=396545161
You can ask there for quick results
hmm.. i think it shld be the same bah.(:
anyone that could help?
1.integrate cot5x / (1+cosec² 5x) dx
factorise something out like mr.wee said
2.it should be: "integrate ((1/cos²
x)+2/(sin² (4x-(π/3))))dx" right? haha.. :)
yeah. sorry, it should be divide. ps
Hi,
I will provide hints to
1. integrate cot5x / (1+cosec² 5x) dx
because it is not obvious.
First, we express both numerator and denominator in terms of sin 5x and cos 5x, which is a very practical strategy in many situations. This will simplify to the expression (sin 5x cos 5x) / {1 + (sin 5x)^2}.
Next, we use the fact that the derivative of 1 + (sin 5x)^2 is 10 sin 5x cos 5x.
Thanks.
Cheers,
Wen Shih
wolfam alpha is also good ... striaght ans for indefinite integrals