MTH301 Quiz 4 January 2026

Question:

Which integral gives the arc length of the curve r(t)=13t3i+tj+t2kr(t)=13t3i+tj+t2kr(t) = \frac{1}{3}{t^3}i + tj + {t^2}k over the interval [1,3]

�A�.� "+�1�3�(�1�+�t�2�)�2""""""""�d�t"+�1�3�(�1�+�t�2�)�2�d�t�\�i�n�t�\�l�i�m�i�t�s�_�1�^�3� �{�\�s�q�r�t� �{�{�{�(�1� �+� �{�t�^�2�}�)�}�^�2�}�}� � �B�.� "+�1�3�(�1�3�+�t�)�2""""""""�d�t"+�1�3�(�1�3�+�t�)�2�d�t�\�i�n�t�\�l�i�m�i�t�s�_�1�^�3� �{�\�s�q�r�t� �{�{�{�(�\�f�r�a�c�{�1�}�{�3�}� �+� �t�)� �C�.� "+�1�3�(�1�+�t�)�2"""""""�d�t"+�1�3�(�1�+�t�)�2�d�t�\�i�n�t�\�l�i�m�i�t�s�_�1�^�3� �{�\�s�q�r�t� �{�{�{�(�1� �+� �t�)�}�^�2�}�}� �}� �d�t �D�.� "+�1�3�1�+�t"""""�d�t"+�1�3�1�+�t�d�t�\�i�n�t�\�l�i�m�i�t�s�_�1�^�3� �{�\�s�q�r�t� �{�1� �+� �t�}� �}� �d�t Copied: 1/6/2026, 12:32:12 PM

Question:

Graph of c=x0i+y0j+z0kGraph of c=x0i+y0j+z0kGraph~ of~ c = {x_0}i + {y_0}j + {z_0}k

A. None of these B. is the curve passing through the point (x0,y0,z0)(x0,y0,z0)( {x_0}, {y_0}, {z_0}) C. is the line passing through the point (x0,y0,z0)(x0,y0,z0)( {x_0}, {y_0}, {z_0}) D. is the point (x0,y0,z0)(x0,y0,z0)( {x_0}, {y_0}, {z_0}) Copied: 1/6/2026, 12:32:47 PM

Question:

If the integration is carried out along the path of a particular curve, such an integral is called . . . . . . . . .

A. Line integral. B. Indefinite integral. C. Surface integral. D. Volume integral. Copied: 1/6/2026, 12:33:03 PM

Question:

The arc length of the portation of the circular helix where and and , then the arc lenght is

A. L = \int\limits_0^\pi {\sqrt 2 } dxL = \int\limits_0^\pi {\sqrt 2 } dx B. L = \int\limits_0^\pi { - \sqrt 2 } dtL = \int\limits_0^\pi { - \sqrt 2 } dt C. L = \int\limits_0^\pi {\sqrt 2 } dyL = \int\limits_0^\pi {\sqrt 2 } dy D. L = \int\limits_0^\pi {\sqrt 2 } dtL = \int\limits_0^\pi {\sqrt 2 } dt Copied: 1/6/2026, 12:33:20 PM

Question:

The vector is continuous at if

A. (a) is defined B. (d) All (a), (b) and (c) . C. (b) exist D. (c) Copied: 1/6/2026, 12:33:47 PM

Question:

If a scalar field exists for all points on the curve, the with , defines the line integral of i .e, line integral =

�A�.� "Á�=�0" �V�(�r�)�d�rÁ"Á�=�0" �V�(�r�)�d�rÁ�\�s�u�m�\�l�i�m�i�t�s�_�{�\�r�h�o� � �=� �0�}�^�\�i�n�f�t�y� � �{�V�(�r�)�d�{�r�_�\�r�h�o� �}�} �B�.� "Á�=�0�n�V�(�r�)�d�rÁ"Á�=�0�n�V�(�r�)�d�rÁ�\�s�u�m�\�l�i�m�i�t�s�_�{�\�r�h�o� � �=� �0�}�^�n� �{�V�(�r�)�d�{�r�_�\�r�h�o� �}�} �C�.� "Á�=�1�n�V�(�r�)�d�rÁ"Á�=�1�n�V�(�r�)�d�rÁ�\�s�u�m�\�l�i�m�i�t�s�_�{�\�r�h�o� � �=� �1�}�^�n� �{�V�(�r�)�d�{�r�_�\�r�h�o� �}�} �D�.� "Á�=�1" �V�(�r�)�d�rÁ"Á�=�1" �V�(�r�)�d�rÁ�\�s�u�m�\�l�i�m�i�t�s�_�{�\�r�h�o� � �=� �1�}�^�\�i�n�f�t�y� � �{�V�(�r�)�d�{�r�_�\�r�h�o� �}�} Copied: 1/6/2026, 12:34:02 PM

Question:

If r is a vector-valued function in 2-space or 3space, then �d�d�t�["+�r�(�t�)�d�t�]�d�d�t�["+�r�(�t�)�d�t�]�{�\�f�r�a�c�{�d�}�{�{�d�t�}�}�\�l�e�f�t�[� �{�\�i�n�t� �{�r�(�t�)�d�t�}� �}� �\�r�i�g�h�t�]�}

�A�.� "+�r�(�t�)�d�t"+�r�(�t�)�d�t�{�\�i�n�t� �{�r�(�t�)�d�t�}� �} �B�.� �d"+�r�(�t�)�d"+�r�(�t�)�d�\�i�n�t� �{�r�(�t�)�} C. r(t)r(t){r(t)} D. None of above Copied: 1/6/2026, 12:34:32 PM

Question:

A line integral naturally involved --------- independent variables in space.