Evaluate : (i) `int_(-oo)^(oo) (dx)/(x^(2)+2x+2)` , (ii) `int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1))`, (iii) `int_(0)^(4)(x^(2))/(1+x)dx` (iv) `int_(0)^(

Question

Evaluate : (i) `int_(-oo)^(oo) (dx)/(x^(2)+2x+2)` , (ii) `int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1))`, (iii) `int_(0)^(4)(x^(2))/(1+x)dx` (iv) `int_(0)^(

Evaluate :
(i) `int_(-oo)^(oo) (dx)/(x^(2)+2x+2)` , (ii) `int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1))`, (iii) `int_(0)^(4)(x^(2))/(1+x)dx`
(iv) `int_(0)^(pi//2) sqrt(costheta)sin^(3)theta`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Related Questions

`int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto` `(sqrt(e))/2(sqrt(3)+1)` (b) `(sqrt(3e))/2` `sqrt(3e)` (d) `sqrt(e/3)`

2 Answers 4 Views

Evaluate : (i) `int_(0)^(1) sin^(-1)((2x)/(1+x^(2)))dx` , (ii) `int_(0)^(1) (xtan^(-1)x)/((1+x^(2))^(3//2))dx` (iii) `int_(a)^(b) sqrt((x-a)(b-x))dx,

2 Answers 4 Views

Evaluate : (i) `int_(-1)^(1)e^(x)dx` , (ii) `int_(-pi//4)^(pi//4)|sinx|dx` , (iii) `int_(-pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx` (iv) `int_(-1)^(1)sin^(

2 Answers 5 Views

Evaluate : (i) `int_(0)^(2pi) {sin(sinx)+sin(cosx)}dx`, (ii) `int_(0)^(pi) (dx)/(5+4cos2x)` (iii) `int_(0)^(pi//2) (2lnsinx-ln sin2x)dx` , (iv) `int_(

2 Answers 5 Views

Evaluate : (i) `int_(-pi//2)^(pi//2)sin^(2)xcos^(2)x(sinx+cosx)dx` , (ii) `int_(0)^(pi)xsin^(5)xdx` (iii) `int_(0)^(2)x^(3//2)sqrt(2-x)dx`, (iv) `int_

2 Answers 5 Views

The value of `sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)]` is equal to `sin^(-1)x+sin^(-1)sqrt(x)` `sin^(-1)x-sin^(-1)sqrt(x)` `sin^(-1)sqrt(x)-sin^(-1)x`

2 Answers 5 Views

Evaluate `(2005int_(0)^(1002)dx(sqrt(1002^(2)-x^(2))+sqrt(1003^(2)-x^(2)))+int_(1002)^(1003)sqrt(1003^(32)-x^(2))dx)/(int_(0)^(1)sqrt(1-x^(2))dx)=k`,

2 Answers 13 Views

If `y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se q u a lto` `(a y)/(xsqrt(a^2-x^2))` (b) `(a y)/(sqrt(a^2-x^2))` `(a y)/(xsqrt(a

2 Answers 4 Views

If `sqrt(2)=1.414, sqrt(3)=1.732` and `sqrt(5)=2.236`, find the values of the following. (i) `sqrt(98)` (ii) `sqrt(300)` (iii) `sqrt(128)+sqrt(48)` (i

2 Answers 4 Views

(i) `(a^(p+q))^(p-q) (a^(q+r))^(q-r)(a^(r+p))^(r-p)` (ii) `[(a/b)^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r))` `[(

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - (i) `pi` , (ii) `pi/4` , (iii) `4 + ln 5` , (iv) `8/21`

5 views Answered 2023-02-05 15:29