• Call Us : 03082533000 (WhatsApp)
  • Email Us : TestPointpk.com@gmail.com
Testpoint Whatsapp group Testpoint Whatsapp group
Sticky Note
What is the value of the integral ∫ e^(x² + ln x) dx ?
  1. (1/2) e^(x²)
  2. e^(x² + x)
  3. x·e^(x²)
  4. None of these
Explanation

What is the value of the integral:

Step 1: Simplify the integrand

Recall:

So,

Step 2: The integral becomes:

Now use substitution:

Let u = x^2 Rightarrow du = 2x , dx Rightarrow frac{1}{2} du = x , dx

So,


int x cdot e^{x^2} , dx = frac{1}{2} int e^u , du = frac{1}{2} e^u + C = frac{1}{2} e^{x^2} + C

Related MCQs

Solve: (2x + 3) / (x - 1) = 3
  1. 3
  2. 5
  3. 6
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
If x = -2 and y = 3, then what is the value of x³y² + x²y?
  1. -72
  2. -60
  3. -48
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Which one is the solution set of |-x| = 0?
  1. {1}
  2. {-1}
  3. {0}
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
During a Hajj field operation, 92 pilgrims form four groups: P is 8 more than Q, R is twice Q, and S is 4 fewer than P. How many are in Group Q?
  1. 18 pilgrims, giving P 26, R 36 and S 22
  2. 14 pilgrims, giving P 22, R 28 and S 18
  3. 16 pilgrims, giving P 24, R 32 and S 20
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
A candidate is participating in a 40-question assessment scoring 2.5 marks per correct answer and deducting 1 per wrong one. He attempts 34 and scores exactly 67. How many were correct?
  1. 26
  2. 28
  3. 27
  4. No whole-number solution exists under the stated scoring system.
اس سوال کو وضاحت کے ساتھ پڑھیں
Test Point Whatsapp Channel

All Rights Reserved © TestPointpk.com