00:01
Hi, here for the given question we are given that we have integration of 14 into under root of sec square minus 16 divided by x to the power 4 dx.
00:13
So here in our case, we need to evaluate this.
00:16
So let us use substitution method.
00:18
Let x is equal to 4 sec theta.
00:20
Now differentiating this we have dx is equal to 4 times sec theta into 10 theta d theta.
00:27
So using the value over here, we have integration 14 times outside under root of 16 sec square theta minus 16 divided by here we have 4 to the power 4 times sec theta as 4 power and here the value is multiplied with sec theta into 10 theta d theta.
00:54
So here now on further reducing this we have value equals to 14 into 4 divided by 4 to the power 4 integration of under root sec square theta minus 1 can be written as 10 square theta taking the root we have 10 theta.
01:09
So 10 theta into sec theta into 10 theta d theta divided by sec to the power 4 theta.
01:16
So here further on reducing this equation here we have value as 14 upon 4 cube integration will be for 10 square theta upon sec cube theta d theta.
01:32
So here now further rearranging the stigmometric function here.
01:37
Now this can be written as 7 upon 64 into 2 which will be 4 square which is 16, 16 into 2 will be 32...