• 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

If 7x = 91, then x is?
  1. 13
  2. 14
  3. 15
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
If 4x − 2y = 10 and 2x + y = 5, then what is the value of x?
  1. 2.5
  2. 3.5
  3. 4.5
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
If (x-2)/3 + (x-4)/10 = x/2, then x = ?
  1. -16
  2. -15
  3. 14
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Maryam has 3 dollars more than Bilal has, but 5 dollars less than Jameel has. If Maryam has x dollars, how many dollars do Jameel and Bilal have altogether?
  1. 2x + 2
  2. 2x - 8
  3. 2x - 5
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Solve: 48 − x = 7x?
  1. x = 5
  2. x = 6
  3. x = 7
  4. None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Test Point Whatsapp Channel

All Rights Reserved © TestPointpk.com