`1/2`
`1`
`sqrt3`
None of the above
`int_0^a g(x) dx`
`int_0^a f(x) dx`
`2 int_0^a f(x) dx`
`0`
`3/2`
`5/2`
`3`
`4`
`1/6`
`1/3`
`5/18`
`5/36`
`37/72`
`2/3`
`17/72`
`37/144`
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
`-1`
`0`
`1`
`2`
`0`
`1`
`2`
`4`
`-3`
`2`
`3`
`5`
`0`
`2`
`4`
`8`
`( x+secx) e^(sinx)+C`
`(x- secx) e^(sinx)+C`
`(x+tanx)e^(sinx)+C`
`(x-tanx)e^(sinx)+C`
`1/4`
`1/2`
`1`
`2`
`(-232)/5`
`(-116)/5`
`(116)/5`
`(232)/5`
`0`
` 2/3`
`2`
` -2`
`2b- a sin (b- a)`
`a+ 3bcos (b- a)`
`sin a- (b- a) cos b`
`0`
`| b|- |a|`
`| a|- |b|`
`(| b|) /(|a|)`
`0`
`8/(15)`
`(16)/(15)`
`(32)/(15)`
`0`
`0`
`1`
`m`
`2m`
Only I
Only II
Both I and II
Neither I nor II
`A = 2B`
`B = 2A`
`A= B`
`A = 3B`
`pi/4`
`pi/2`
`(3pi)/4`
`pi`
`0`
`2`
`-2`
`pi`
`In 2`
`- In 2`
`0`
None of these
` e^(pi/4) - 1`
` e^(pi/4) + 1`
` e - 1`
`e`
`0`
` 2 I_1`
`pi`
None of these
` pi/(24)`
` pi/(18)`
` pi/(12)`
` pi/(6)`
`2 ab`
`2pi ab`
` pi/(2 ab)`
`pi/(ab)`
`tan x - (tan^3 x)/3 + 4x`
`tan x + (tan^3 x)/3 + 4x`
`tan x + (sec^3 x)/3 + 4x`
`- tan x - (tan^3 x)/3 + 4x`
`- pi`
`0`
`pi`
`2 pi`
`pi`
`pi/2`
`0`
`2 pi`
`1`
`2`
`4`
`-2`
`4I`
`2I`
`I`
`I/2`
`I/2`
`I`
`2I`
`4I`
`pi/2`
`pi/4`
`pi/8`
None of these
`a`
`2a`
`0`
`1`
`1`
`-1`
`0`
`e`
`pi/4`
`pi/8`
`pi^2/8`
`pi^2/32`
`2`
`1`
`pi`
`0`
`k = 3`
`0 le k < 3`
`k le 4`
`k = 0`
`1/n`
`1/(n-1)`
`n/(n-1)`
`1/(n-2)`
`pi`
`pi/3`
`pi/sqrt3`
`(2pi)/sqrt3`
`0`
`int_0^(pi/2) f(cosx)dx`
`2int_0^(pi/2) f(cosx)dx`
`1`
`2 ln sqrt3`
`ln sqrt3`
`2 ln 3`
`4 ln 3`
`e(e/2-1)`
`e(e-1)`
`e-1/e`
`0`
`1`
`0`
`2`
`-1`
`pi`
`pi/2`
`pi/4`
`0`
`x^3/3-x+4 tan^(-1) x+C`
`x^3/3+x+4 tan^(-1)+C`
`x^3/3-x+2 tan^(-1) x+C`
`x^3/3-x-4 tan^(-1) x+C`
`1/3` and `-1/9`
`3` and `-9`
`3` and `9`
`3` and `3`
`x-log x +C`
`x-log (tan x)+C`
`x-log(1+e^x)+C`
`log (1+e^x)+C`
Values of x only
Values of each of a, b and c
Value of c only
Value of b only
`1/2` and `2`
`-1/2` and `2`
`1/2` and `-2`
`-1/2` and `-2`
`(e-1)/2`
`e^2-1`
`2(e-1)`
`e-1`
`ln (ex + 1) + C`
`ln (e^(-x) + 1) + C`
`-ln (e^(-x) + 1) + C`
`-(ex + 1) + C`
`tan theta+c`
`cot theta+C`
`1/2 tan theta+C`
`1/2 cot theta+C`
`1/110`
`1/111`
`1/112`
`1/119`
`(35 pi)/256`
`70/256`
`16/35`
`(8pi)/35`
`e^2`
`1/e`
`ln4`
`1`
`-19/6`
`19/6`
`3/2`
`-3/2`
Assertion : (A) `int_0^(pi) sin^7 xdx = 2int_0^(pi/2) sin^7 xdx`
Reason : (R) `sin^7 x` is odd function