COMPACT QUESTIONS INTEGRATION

EXERCISE -A

1) ∫ dx/(1+ sinx).             Tanx- sex+ c

2) ∫ (tanx - x)tan²x.      1/2 (tanx - x)²+ c

3) State formula for integration by parts.   

4) ∫ dx/(sin²x cos²x).                       tanx- cotx +c

5) Integrate logx w.r.to x.            xlogx - x+ c


EXERCISE -B

1) The value of ∫ dx/(sinx cosx) is
a) log|cotx| b)  log|tanx|   c) log|secx| d) log|sinx|

2) The value of ∫ (sinx+ cosx)/√(1+ sin2x) dx is
a) sinx b) x c) cosx d) tanx



EXERCISE - C

1) ∫ sin2x/(sin3xsin5x) dx.        1/3 log|sin3x| - 1/5 log|sin5x|+ c

2) ∫ dx/{sin(x -α) sin(x -β)}.      1/sin(x -α)  log|sin(x -α) sin(x-β)|+ c

3) ∫ (sinx + cosx)/sin(x -α) dx.           (Cosα - sinα)(x -α) + cos + sinα) log|sin(x -α)|+ c

4) ∫ tanx tan2x tan3x dx.                   1/3 log|sec3x| -1/2 log|sec2x| - log|secx| + c

5) ∫ √tanx/(sinxcosx) dx.                    2√tanx + c

6) ∫ dx/(√(2ax - x²) (x> a).    sin⁻{(x- a)/a + c

7) ∫ dx/{√(x+1) + ³√(x+1)}.        2√(x+1) - 3 ³√(x+1)+ 6 ⁶√(x+1) - 6 log|⁶√(x+1)+1|+ c

8) ∫ x²/{(x²+1)(x -1)²} dx.        1/2 [log|x -1| - 1/(x -1) - 1/2 log(x²+1)] + c

9) ∫ d(x²-1)/{x√(2- x²)}.               sin⁻¹ √(x²-1)+ c

10) ∫ dx/(eˣ + e⁻ˣ).                   tan⁻¹eˣ + c

11) ∫ (x²+ sin²x)sec²x/(1+ x²) dx.       tanx - tan⁻x+ c

12) ∫ (x + sinx)/(1+ cosx) dx.         x tan(x/2)+ c

13) ∫ xeˣ/(x+1)²dx.         eˣ/(x+1) + c

14) ∫ {log(1+ x²)}/(1+ x)² dx.      (1/2 - 1/(x+1) log(1+ x²)+ tan⁻¹x - log|1+ x| + c

15) ∫ sin⁻¹√{x/(x+ a)} dx.        (x+ a)ta(x/a) - √(ax) + c

16)  ∫ sinx/(sinx + cosx) dx.        1.2 [x - log|sinx + cosx|] + c

17) ∫ dx/{2x-7)√(x²- 7x+12)}.              Sec⁻(2x -7)+ c

18) ∫ sin(logx) dx.      x/2[sin(logx)- cos(logx)]+ c

19) ∫ dx/{2x - x²)√(2x - x²)}.          (x-1)/√(2x - x²)+ c

20) ∫ dx/{(x+ a)(x²+ a²)}.            1/2a²[log|x + a| - 1/2 log(x²+ a²)+ tan⁻¹(x/a) ]+ c

EXERCISE - D

1) ∫ √(1+ cosec2x) dx.               2sin⁻¹(sinx/2 - cosx/2)+ c

2) ∫ (cosx + x sinx)/(x(x+ cosx)) dx.        Log(x/(x + cosx)+ c

3) ∫ dx/(cos⁴x - cos²x sin²x + sin⁴x).       tan⁻¹(tanx - cotx)+ c

4)  ∫ ₑtan⁻¹x {(1+ x + x²)/(1+ x²)} dx.        ₑtan⁻¹x  + c

5) ∫ dx/(sina + sinx), a being constant.        1/cosa [log|sin(1/2)(x+a)| - log|cos(1/2)(x - a)|] + c

6)  ∫ (1- x²)/(1+ x²) . dx/√(1+ x²+ x⁴).         cosec⁻¹(x + 1/x)+ c

7)  ∫ (x -1)/(x+1) dx/√(x + x²+ x³).        2tan⁻¹√(x+ 1/x +1) + c.

8) ∫ dx/√{sin³x sin(x + a)}.                 - 2 cosec a√(sin(x+ a)cosec2x)+ c

9) ∫ eˢᶦⁿˣ(x cosx - secxtanx) dx.           (x - secx) eˢᶦⁿˣ+ c

10) ∫ (cosx - sinx)/√sin2x  dx.      log|sinx + cosx+ √sin2x| + c

11) ∫ √tanx dx.        1/√2 sin⁻¹ (sinx - cosx) - 1/√2 log|sinx + cosx + √sin2x| + c

12) Prove ∫ x²dx/(x sinx + cosx)² = (sinx - x cosx)/(xsinx + cosx)+ c


Comments

Post a Comment

Popular posts from this blog

REVISION - XII

DETERMINANT  1) If two rows or two columns of a determinant are identical then the value of the determinant is a) 0 b) 2 c) -1 d) 1 2) If D= 0     a    b              -a     0    c              -b    -c    0 then D is  a) 0 b) 1 c) a d) b 3) a+b    a+2b    a+3b     a+2b  a+3b    a+4b= 0     a+4b  a+5b     a+6b 4 ) 1+ a      1        1       1       1+ b     1        1         1      1+ c = abc(1/a + 1/b + 1/c) 5) loga       p      1     logb       q       1 = 0 (a,b,c> 0)     logc       r     ...
Read more

SHORT QUESTIONS- X (All chapter)

Image
GOODS AND SERVICES TAX Multiple Choice Questions 1) IGST is charged on: a) interstate transaction b) intrastate transaction c) both a, b d) none 2) GST payable is equals to a)  ITC --output GST b) output GST + ITC c) output GST - ITC d) output GST 3) A dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000. If the rate of GST is 18% and GST, then SGST is: a) Rs1620 b) Rs3240 c) nil d) none 4) In a transaction from Delhi to Lucknow, MRP = Rs10000, discount= 10%, GST= 28%. Here IGST is: a)  Rs2520 b) Rs5040 c) nil  d) none 5) A refrigerator was sold for Rs15000 under intrastate transaction from station A to station B and the GST rate is 18%. CGST is: a) Rs1450 b) Rs 1350 c) Rs1300 d) Rs2700  6) A dealer purchased goods worth Rs 15000 and sold them for Rs21000 within the state. If the rate of GST is 12%, then the net SGST paid by the dealer is: a) Rs360 b) Rs720 c) Rs800 d) Rs850  7) A dealer in Delhi sold a water heater whose marked is Rs22000...
Read more

MULTIPLE CHOICE QUESTIONS -XII

MAXIMUM AND MINIMUM 1) The minimum value of f(x)= x²+ 250/x is a) 55  b) 25 c) 50 d) 75  2) If  f(x)=  1/(4x²+ 2x +1) , then its maximum value is  a) 2/3 b) 4/3  c) 3/4 d) 1  3) The function  f(x)=  2x³- 3x²- 12x +4 has a) no maximum and minimum b) one maximum and one minimum  c) two maximum d)  two minimum  4) The height of the cylinder of maximum volume that can be inscribed in a sphere of radius a is  a) 3a/2  b) √2a/3 c) 2 a/√3 d)  a/√3 5) Maximum value of (logx)/x in [0,∞) is a) (log2)/2 b) 0 c) 1/e d) e 6) let the function f: R--> R be defined by f(x)= 2x + cosx; then f(x).. a) has maximum value at x=0. b) has minimum value at x=π c) is a decreasing function d) is an increasing function  7) The maximum distance from the origin of a point on the curve x= a sin t - b sin(at/b), y= a cos t - b cos(at/b), both a, b> 0, is a) a- b b) a+ b c) √(a²+ b²) d) √(a²- b²) 8) Let x and y be two variables and x...
Read more